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In mathematics and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi-Yau manifolds. It can happen, for two such six-dimensional manifolds, that their shapes look very different geometrically, but nevertheless they are equivalent if they are employed as hidden dimensions of string theory.^[1] In this case, the six-dimensional manifolds are said to be "mirror" to one another.

Mirror symmetry was originally discovered by physicists. Mathematicians became interested in mirror symmetry around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parks showed that mirror symmetry could be used to count rational curves on a Calabi-Yau manifold, thus solving a longstanding problem.^[2] Although the original approach to mirror symmetry was based on nonrigorous ideas from theoretical physics, mathematicians have gone on to rigorously prove some of the mathematical predictions of mirror symmetry.^[3]

Today mirror symmetry is a major research topic in pure mathematics, and mathematicians are working to develop a mathematical understanding of mirror symmetry based on physicists' intuition.^[4] Mirror symmetry is also a fundamental tool for doing calculations in string theory.^[5] Major approaches to mirror symmetry include homological mirror symmetry program of Maxim Kontsevich^[6] and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow.^[7]

Overview

The idea of mirror symmetry

Mirror symmetry is a particular example of what physicists call a duality.^[8] In physics, the term duality refers to a situation where two seemingly different physical systems turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory. The two theories are then said to be dual to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena.

Like many of the dualities studied in theoretical physics, mirror symmetry was discovered in the context of string theory.^[9] In string theory, particles are modeled not as zero-dimensional points but as one-dimensional extended objects called strings. One of the peculiar features of string theory is that it requires extra dimensions of spacetime for its mathematical consistency. In superstring theory, the version of the theory that incorporates worldsheet supersymmetry, there are six extra dimensions of spacetime in addition to the four that are familiar from everyday experience.^[10]

In most realistic models of physics based on string theory, the extra dimensions are eliminated from the theory at low energies by a process known as compactification. This produces a theory in which spacetime has effectively a lower number of dimensions and the extra dimensions are "curled up" into complex shapes called Calabi-Yau manifolds.^[11] A standard analogy for this is to consider multidimensional object such as a garden hose.^[12] If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions. In certain models based on string theory, the Calabi-Yau manifolds play a role analogous to the circumference of the hose.

In the late 1980s, it was noticed that given such a compactification of string theory, it is not possible to uniquely reconstruct a corresponding Calabi-Yau manifold. Instead, one finds that there are two Calabi-Yau manifolds that give rise to the same physics.^[13] These manifolds are said to be "mirror" to one another. Although the full duality is still only a conjecture, there is a version of mirror symmetry in the context of topological string theory, a simplified version of string theory introduced by Edward Witten,^[14] and this version has been rigorously proven by mathematicians.^[15] In the context of topological string theory, mirror symmetry states that two theories, the A-model and B-model, are equivalent in a certain precise sense.^[16]

Regardless of whether these Calabi-Yau compactifications of string theory provide a correct description of nature, the existence of the mirror symmetry relationship between different Calabi-Yau manifolds has significant mathematical consequences.^[17] The Calabi-Yau manifolds used in string theory are of interest in pure mathematics, and mirror symmetry allows mathematicians to solve many problems in enumerative algebraic geometry by solving equivalent problems for the mirror Calabi-Yau.^[18] Today mirror symmetry is an active area of research in mathematics, and mathematicians are still working to develop a mathematical understanding of mirror symmetry based on physicists' intuition.^[19]

Complex geometry

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To understand the kind of geometry that appears on one side of the mirror duality, we will consider here a construction of a torus, a closed surface with a single hole like a donut, by identifying points of the complex plane. To construct this torus, we first choose a pair of complex numbers $\omega _{1}$ and $\omega _{2}$ such that the quotient $\omega _{1}/\omega _{2}$ is not real. This last condition ensures that these points are not collinear. Then the chosen points determine a parallelogram whose other vertices are 0 and $\omega _{1}+\omega _{2}$ . By identifying opposite sides of this parallelogram, we obtain the desired torus.

The tori obtained in this way are all equivalent in the sense that we can continuously deform one torus into another.^[20] On the other hand, they have an additional structure which allows us to distinguish them.^[21] Namely, the tori constructed in this way have a complex structure, meaning that a neighborhood of any point on such a torus looks just like a region in the complex plane.

If in the construction of a torus we had instead used a pair of complex numbers $\omega _{1}'$ and $\omega _{2}'$ related to the original pair by rescaling by a common factor (that is, $\omega _{1}'=\lambda \omega _{1}$ and $\omega _{2}'=\lambda \omega _{2}$ for some complex number $\lambda$ ), then we would get an equivalent torus. It is therefore more convenient to parametrize the collection of tori by the ratio $\tau =\omega _{1}/\omega _{2}$ , which does not change when we rescale the $\omega _{i}$ . One can assume, without loss of generality, that this parameter $\tau$ has positive imaginary part so that $\tau$ takes values in the upper half plane. One can also show that the parameters $\tau$ , $\tau +1$ , and $-1/\tau$ correspond to the same torus.

If two tori correspond to genuinely different values of $\tau$ , then they have inequivalent complex structures.^[22] One can think of the parameter $\tau$ as describing the "shape" of a torus constructed by identifying opposite sides of a parallelogram. As explained above, mirror symmetry relates two physical theories, the A- and B-models of topological string theory. In this duality, the topological B-model depends only on the complex structure of spacetime. Thus, if we consider the theory in which "spacetime" is a torus, the theory will depend continuously only on the parameter $\tau$ .^[23]

Symplectic geometry

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Another aspect of the geometry of a torus is the size of the torus. More precisely, we can talk view a torus as the surface obtained by identifying opposite sides of a unit square, and the area of the torus is specified by an area element $\rho dxdy$ on this square. By integrating this area element over the unit square, we obtain the area $\rho$ of the corresponding torus. These concepts can be generalized to higher dimensions, and the area element is generalized by the notion of a symplectic form. The study of spaces equipped with a symplectic form is called symplectic geometry.

In mirror symmetry, the A-model of topological string theory is a theory that depends only on the symplectic geometry of spacetime. Thus, if we consider the theory in which "spacetime" is a torus, then the A-model depends continuously only on the parameter $\rho$ .^[24]

T-duality

A torus is the product of two circles, in this case the red circle is swept around axis defining the pink circle. $R_{1}$ is the radius of the red circle, $R_{2}$ is the radius of the pink one.

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We have now seen how a torus can be obtained by identifying opposite sides of a parallelogram in the complex plane. A particularly simple example is where the complex numbers $\omega _{1}$ and $\omega _{2}$ lie on the real and imaginary axes, respectively. In this case, we can write $\omega _{1}=R_{1}$ and $\omega _{2}=iR_{2}$ where $R_{1}$ and $R_{2}$ are real numbers. As discussed above, the complex structure on the torus obtained in this way is characterized by the number $\tau =iR_{2}/R_{1}$ .

We have explained how the symplectic structure of the torus is determined by an area element. We can choose coordinates $x$ and $y$ on our parallelogram so that each side of the parallelogram spanned by the chosen complex numbers has length 1. Then the area element of our torus is $R_{1}R_{2}dxdy$ which integrates to $R_{1}R_{2}$ on the unit square. We define the symplectic parameter $\rho$ to be the product $iR_{1}R_{2}$ .

Note that the torus can also be considered as a cartesian product of two circles. This means that at each point of an equatorial circle on the torus (illustrated in pink), there is a longitudinal circle (illustrated in red).

Let us now imagine that the torus represents the "spacetime" for a physical theory. The fundamental objects of this theory will be strings propagating through the spacetime according to the rules of quantum mechanics. One of the basic dualities of string theory is T-duality, which states that a string propagating around a circle of radius $R$ is equivalent to a string propagating around a circle of radius $1/R$ in the sense that all observable quantities in one description are identified with quantities in the dual description.^[25] For example, the momentum of a string in one description takes discrete values and is equal to the number of times the string winds around the circle in the dual description.^[26] Applying T-duality to the longitudinal circle on the torus, we find that there is an equivalent description in which spacetime is represented by a different torus. The duality changes $R_{1}$ to $1/R_{1}$ , and thus it interchanges the complex and symplectic parameters:

\tau \leftrightarrow \rho

.

In general, mirror symmetry is an equivalence of two physical theories that translates problems in complex geometry into problems in symplectic geometry. The torus considered here is the only compact Calabi-Yau manifold of (real) dimension two and is therefore the simplest example of mirror symmetry.^[27] In applications to string theory, one usually considers a six-dimensional Calabi-Yau manifold, where the six dimensions correspond to the six unobserved dimensions of spacetime.

Applications of mirror symmetry

Enumerative geometry

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Many of the important mathematical applications of mirror symmetry belong to the branch of mathematics called enumerative geometry. In enumerative geometry, one is interested in counting the number of solutions to geometric questions, typically using the techniques of algebraic geometry. One of the earliest problems of enumerative geometry was posed around the year 200 BCE by the ancient Greek mathematician Apollonius, who asked how many circles in the plane are tangent to three given circles.^[28] In general, the solution to the problem of Apollonius is that there are eight such circles. The picture on the right shows an example where the three given circles are illustrated in black.

Enumerative problems in mathematics often concern a class of geometric objects called algebraic varieties which are defined by the vanishing of polynomials. For example, the Clebsch cubic is the surface illustrated on the left which is defined using a certain polynomial of degree three in four variables. A celebrated result of nineteenth-century mathematicians Arthur Cayley and George Salmon states that there are exactly 27 straight lines that lie entirely on such a surface.^[29]

Generalizing this problem, one can ask how many lines can be drawn on a quintic such as the Calabi-Yau illustrated above. This problem was solved by the nineteenth-century German mathematician Hermann Schubert, who found that there are exactly 2,875 such lines. In 1986, geometer Sheldon Katz proved that the number of curves of degree two (such as circles) which lie entirely in the quintic is 609,250.^[30]

By the year 1991, most of the classical problems of enumerative geometry had been solved and interest in enumerative geometry had begun to diminish. According to mathematician Mark Gross, "As the old problems had been solved, people went back to check Schubert's numbers with modern techniques, but that was getting pretty stale."^[31] The field was reinvigorated in May 1991 when physicists Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parks showed that mirror symmetry could be used to count the number of degree three curves lie on a quintic Calabi-Yau. Roughly speaking, one can think of such a degree three curve as a sphere that lies entirely inside the Calabi-Yau.^[32] Candelas and his collaborators found that such these six-dimensional Calabi-Yau manifolds can contain exactly 317,206,375 curves of degree three.^[33]

In addition to counting degree-three curves on a quintic three-fold, Candelas and his collaborators obtained a number of more general results for counting rational curves which went far beyond the results obtained by mathematicians.^[34] Although the methods used in this work were based on nonrigorous ideas from theoretical physics, mathematicians have gone on to rigorously prove some of the predictions of mirror symmetry. In particular, the enumerative predictions of mirror symmetry have now been rigorously proven.^[35]

String theory

In addition to its applications to enumerative geometry, mirror symmetry is a fundamental tool for doing calculations in string theory. When a calculation in string theory is impossible using the techniques of perturbation theory, theorists can apply dualities such as mirror symmetry to translate the calculation into an equivalent calculation in a different theory. By outsourcing calculations to different theories in this way, theorists can calculate many quantities that are impossible to calculate without the use of dualities.^[36]

Approaches to mirror symmetry

Homological mirror symmetry

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In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions.^[37] For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher dimensional branes. The word brane comes from the word "membrane" which refers to a two-dimensional brane.

In string theory, a string may be open (forming a segment with two endpoints) or closed (forming a closed loop). D-branes are an important class of branes that arise when one considers open strings.^[38] As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to the fact that we impose a certain mathematical condition on the system known as the Dirichlet boundary condition.

Mathematically, branes can be described using the notion of a category.^[39] This is a mathematical structure consisting of objects, and for any pair of objects, a set of morphisms between them. In most examples, the objects are mathematical structures of some kind (for example, sets, vector spaces, or topological spaces) and the morphisms are given by functions between these structures.^[40] We can also consider categories where the objects are D-branes and the morphisms between two branes $\alpha$ and $\beta$ are wavefunctions of open strings stretched between $\alpha$ and $\beta$ .^[41]

In the B-model of topological string theory, the category of D-branes is constructed from the complex geometry of the Calabi-Yau manifold on which the strings propagate. In mathematical language, it is known as the derived category of coherent sheaves on the Calabi-Yau. On the other hand, the category of D-branes in the A-model is constructed from the symplectic geometry of the mirror Calabi-Yau. It is known in mathematics as the Fukaya category.^[42] The homological mirror symmetry conjecture of Maxim Kontsevich states that these two categories of branes are equivalent in a certain sense.^[43]

Strominger-Yau-Zaslow conjecture

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Another approach to understanding mirror symmetry was suggested by Andrew Strominger, Shing-Tung Yau, and Eric Zaslow in 1996.^[44] According to the SYZ conjecture, mirror symmetry can be understood by dividing a complicated Calabi-Yau manifold into simpler pieces and considering the effects of T-duality on these pieces.^[45]

Recall that in the Overview section we considered the case of a torus, and we viewed this torus as the product of two circles. This means that the torus can be viewed as the union of a collection of longitudinal circles (such as the red circle in the image). There is an auxiliary space which says how these circles are organized, and this space is itself a circle (the pink circle). This space is said to parametrize the longitudinal circles on the torus. As explained above, mirror symmetry is equivalent to T-duality acting on the longitudinal circles, changing their radii from $R_{1}$ to $1/R_{1}$ .

The SYZ conjecture generalizes this idea to the more complicated case of six-dimensional Calabi-Yau manifolds. As in the case of a torus, we can divide a six-dimensional Calabi-Yau into simpler pieces, which in this case are 3-tori (three-dimensional objects which generalize the notion of a torus) parametrized by a 3-sphere (a three-dimensional generalization of a sphere).^[46] T-duality can be extended from circles to the three-dimensional tori appearing in this decomposition, and the SYZ conjecture states that mirror symmetry is equivalent to the simultaneous application of T-duality to these three-dimensional tori.^[47] In this way, the SYZ conjecture provides a geometric picture of how mirror symmetry acts on a Calabi-Yau manifold.

History

The idea of mirror symmetry can be traced back to the mid-1980s when it was noticed that a string propagating on a circle of radius $R$ is physically equivalent to a string propagating on a circle of radius $1/R$ in appropriate units.^[48] This phenomenon is now known as T-duality and is understood to be closely related to mirror symmetry.

In a paper from 1985, Philip Candelas, Gary Horowitz, Andrew Strominger, and Edward Witten showed that by compactifying string theory on a Calabi-Yau manifold, one obtains a theory roughly similar to the standard model of particle physics.^[49] Following this development, many physicists began studying Calabi-Yau compactifications, hoping to construct realistic models of particle physics based on string theory. It was noticed that given such a physical model, it is not possible to uniquely reconstruct a corresponding Calabi-Yau manifold. Instead, one finds that there are two Calabi-Yau manifolds that give rise to the same physics.^[50]

Mathematicians became interested in mirror symmetry around 1990 when physicists Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parks showed that mirror symmetry could be used to solve certain problems in enumerative geometry, some of which had resisted solution for decades or more.^[51] These results were presented to mathematicians at a conference at the Mathematical Sciences Research Institute (MSRI) in Berkeley, California in May 1991. During this conference, it was noticed that one of the numbers Candelas had computed for the problem of counting rational curves disagreed with the number obtained by Norwegian mathematicians Geir Ellingsrud and Stein Arild Strømme using ostensibly more rigorous techniques.^[52] Many mathematicians at the conference assumed that Candelas's work contained a mistake since it was not based on rigorous mathematical arguments. However, after examining their solution, Ellingsrud and Strømme discovered an error in their computer code and, upon fixing the code, they got an answer that agreed with the one obtained by Candelas and his collaborators.^[53]

In 1990, Edward Witten introduced topological string theory,^[54] a simplified version of string theory, and physicists showed that there is a version of mirror symmetry for topological string theory.^[55] This statement about topological string theory is usually taken as the definition of mirror symmetry in the mathematical literature.^[56] In an address at the International Congress of Mathematicians in 1994, mathematician Maxim Kontsevich presented a new mathematical conjecture based on the physical idea of mirror symmetry in topological string theory. Known as homological mirror symmetry, this conjecture formalizes mirror symmetry as an equivalence of two mathematical structures: the derived category of coherent sheaves on a Calabi-Yau manifold and the Fukaya category of its mirror.^[57]

Also around 1995, Kontsevich analyzed the results of Candelas, which gave a general formula for the problem of counting rational curves on a quintic threefold, and he reformulated these results as a precise mathematical conjecture. In 1996, Alexander Givental posted a paper which claimed to prove this conjecture of Kontsevich.^[58] Initially, many mathematicians found this paper hard to understand, and so there were doubts about the correctness of Givental's proof. In the years following this, Bong Lian, Kefeng Liu, and Shing-Tung Yau published an independent proof in a series of papers.^[59] Despite some controversy over who had published the first proof, these papers are now seen as providing a mathematical proof of the results originally obtained by physicists using mirror symmetry.^[60]

Notes

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References

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The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

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Contents

Overview

The idea of mirror symmetry

Complex geometry

Symplectic geometry

T-duality

Applications of mirror symmetry

Enumerative geometry

String theory

Approaches to mirror symmetry

Homological mirror symmetry

Strominger-Yau-Zaslow conjecture

History

See also

Notes

References

Further reading

Popularizations

Textbooks

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+{{String theory}}
+In [[mathematics]] and [[theoretical physics]], '''mirror symmetry''' is a relationship between [[geometry|geometric]] objects called [[Calabi-Yau manifold]]s. It can happen, for two such six-dimensional [[manifolds]], that their shapes look very different geometrically, but nevertheless they are equivalent if they are employed as hidden dimensions of [[string theory]].<ref>Yau and Nadis 2010</ref> In this case, the six-dimensional manifolds are said to be "mirror" to one another.
+Mirror symmetry was originally discovered by physicists. Mathematicians became interested in mirror symmetry around 1990 when [[Philip Candelas]], Xenia de la Ossa, Paul Green, and Linda Parks showed that mirror symmetry could be used to count [[rational curve]]s on a Calabi-Yau manifold, thus solving a longstanding problem.<ref>Yau and Nadis 2010</ref> Although the original approach to mirror symmetry was based on [[mathematical rigor|nonrigorous]] ideas from theoretical physics, mathematicians have gone on to [[mathematical proof|rigorously prove]] some of the mathematical predictions of mirror symmetry.<ref>Givental 1996, 1998; Lian, Liu, Yau 1997, 1999, 2000</ref>
+Today mirror symmetry is a major research topic in [[pure mathematics]], and mathematicians are working to develop a mathematical understanding of mirror symmetry based on physicists' intuition.<ref>Hori et al. 2003; Aspinwall et al. 2009</ref> Mirror symmetry is also a fundamental tool for doing calculations in string theory.<ref>Zaslow 2008</ref> Major approaches to mirror symmetry include [[homological mirror symmetry]] program of [[Maxim Kontsevich]]<ref>Kontsevich 2005</ref> and the [[SYZ conjecture]] of [[Andrew Strominger]], [[Shing-Tung Yau]], and [[Eric Zaslow]].<ref>Strominger, Yau, and Zaslow 1996</ref>
+==Overview==
+===The idea of mirror symmetry===
+Mirror symmetry is a particular example of what physicists call a [[duality (physics)|duality]].<ref>Hori et al. 2003, p. xiv</ref> In physics, the term ''duality'' refers to a situation where two seemingly different [[physical system]]s turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory. The two theories are then said to be ''dual'' to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena.
+Like many of the dualities studied in [[theoretical physics]], mirror symmetry was discovered in the context of [[string theory]].<ref>Other dualities that arise in string theory are [[S-duality]], [[T-duality]], [[U-duality]], and the [[AdS/CFT correspondence]].</ref> In string theory, particles are modeled not as zero-dimensional points but as one-dimensional extended objects called [[string (physics)|strings]]. One of the peculiar features of string theory is that it requires [[extra dimensions]] of [[spacetime]] for its mathematical consistency. In [[superstring theory]], the version of the theory that incorporates [[supersymmetry|worldsheet supersymmetry]], there are six extra dimensions of [[spacetime]] in addition to the four that are familiar from everyday experience.<ref>Zwiebach 2009, p.8</ref>
+[[Image:Calabi yau.jpg|left|thumb|200px|A three-dimensional projection of a [[Calabi–Yau manifold]]. ]]
+In most realistic models of physics based on string theory, the extra dimensions are eliminated from the theory at low energies by a process known as [[compactification (physics)|compactification]]. This produces a theory in which spacetime has effectively a lower number of dimensions and the extra dimensions are "curled up" into complex shapes called [[Calabi-Yau manifolds]].<ref>Yau and Nadis 2010, Ch.6</ref> A standard analogy for this is to consider multidimensional object such as a garden hose.<ref>This analogy is used for example in Greene 2000, p.186</ref> If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions. In certain models based on string theory, the Calabi-Yau manifolds play a role analogous to the circumference of the hose.
+In the late 1980s, it was noticed that given such a compactification of string theory, it is not possible to uniquely reconstruct a corresponding Calabi-Yau manifold. Instead, one finds that there are ''two'' Calabi-Yau manifolds that give rise to the same physics.<ref>Dixon 1988; Lerche, Vafa, and Warner 1989</ref> These manifolds are said to be "mirror" to one another. Although the full duality is still only a conjecture, there is a version of mirror symmetry in the context of [[topological string theory]], a simplified version of string theory introduced by [[Edward Witten]],<ref>Witten 1990</ref> and this version has been [[mathematical rigor|rigorously proven]] by mathematicians.<ref>Givental 1996, 1998; Lian, Liu, Yau 1997, 1999, 2000</ref> In the context of topological string theory, mirror symmetry states that two theories, the A-model and B-model, are equivalent in a certain precise sense.<ref>Zaslow 2008, p.531</ref>
+Regardless of whether these Calabi-Yau compactifications of string theory provide a correct description of nature, the existence of the mirror symmetry relationship between different Calabi-Yau manifolds has significant mathematical consequences.<ref>Zaslow 2008, p.523</ref> The Calabi-Yau manifolds used in string theory are of interest in pure mathematics, and mirror symmetry allows mathematicians to solve many problems in [[enumerative geometry|enumerative algebraic geometry]] by solving equivalent problems for the mirror Calabi-Yau.<ref>Yau and Nadis 2010, p.168</ref> Today mirror symmetry is an active area of research in mathematics, and mathematicians are still working to develop a mathematical understanding of mirror symmetry based on physicists' intuition.<ref>Hori et al. 2003, p. xix</ref>
+===Complex geometry===
+{{main|Complex geometry}}
+[[File:Torus.png|left|thumb|A torus]]
+To understand the kind of geometry that appears on one side of the mirror duality, we will consider here a construction of a [[torus]], a closed surface with a single hole like a donut, by identifying points of the [[complex plane]]. To construct this torus, we first choose a pair of complex numbers <math>\omega_1</math> and <math>\omega_2</math> such that the quotient <math>\omega_1/\omega_2</math> is not [[real number|real]]. This last condition ensures that these points are not [[collinear]]. Then the chosen points determine a [[parallelogram]] whose other [[vertex (geometry)|vertices]] are 0 and <math>\omega_1+\omega_2</math>. By identifying opposite sides of this parallelogram, we obtain the desired torus.
+[[Image:Lattice torsion points.svg|right|thumb|300px| A [[torus]] can be constructed by identifying opposite sides of a [[parallelogram]] in the [[complex plane]]. This torus inherits a [[complex manifold|complex structure]] which, roughly speaking, describes the "shape" of the torus. ]]
+The tori obtained in this way are all equivalent in the sense that we can [[homotopy|continuously deform]] one torus into another.<ref>Zaslow 2008, p.530</ref> On the other hand, they have an additional structure which allows us to distinguish them.<ref>Zaslow 2008, p.531</ref> Namely, the tori constructed in this way have a [[complex manifold|complex structure]], meaning that a neighborhood of any point on such a torus looks just like a [[domain (mathematical analysis)|region]] in the complex plane.
+If in the construction of a torus we had instead used a pair of complex numbers <math>\omega_1'</math> and <math>\omega_2'</math> related to the original pair by rescaling by a common factor (that is, <math>\omega_1'=\lambda\omega_1</math> and <math>\omega_2'=\lambda\omega_2</math> for some complex number <math>\lambda</math>), then we would get an equivalent torus. It is therefore more convenient to parametrize the collection of tori by the ''ratio'' <math>\tau=\omega_1/\omega_2</math>, which does not change when we rescale the <math>\omega_i</math>. One can assume, [[without loss of generality]], that this parameter <math>\tau</math> has positive [[imaginary part]] so that <math>\tau</math> takes values in the [[upper half plane]]. One can also show that the parameters <math>\tau</math>, <math>\tau+1</math>, and <math>-1/\tau</math> correspond to the same torus.
+If two tori correspond to genuinely different values of <math>\tau</math>, then they have inequivalent complex structures.<ref>More precisely, tori are parametrized by the [[fundamental domain]] for the [[modular group]].</ref> One can think of the parameter <math>\tau</math> as describing the "shape" of a torus constructed by identifying opposite sides of a parallelogram. As explained above, mirror symmetry relates two physical theories, the A- and B-models of [[topological string theory]]. In this duality, the topological B-model depends only on the complex structure of [[spacetime]]. Thus, if we consider the theory in which "spacetime" is a torus, the theory will depend continuously only on the parameter <math>\tau</math>.<ref>Zaslow 2008, p.531</ref>
+===Symplectic geometry===
+{{main|Symplectic geometry}}
+Another aspect of the geometry of a torus is the size of the torus. More precisely, we can talk view a torus as the surface obtained by identifying opposite sides of a unit square, and the area of the torus is specified by an [[area element]] <math>\rho dxdy</math> on this square. By [[integral|integrating]] this area element over the [[unit square]], we obtain the [[area]] <math>\rho</math> of the corresponding torus. These concepts can be generalized to higher dimensions, and the area element is generalized by the notion of a [[symplectic form]]. The study of spaces equipped with a symplectic form is called [[symplectic geometry]].
+In mirror symmetry, the A-model of [[topological string theory]] is a theory that depends only on the symplectic geometry of [[spacetime]]. Thus, if we consider the theory in which "spacetime" is a torus, then the A-model depends continuously only on the parameter <math>\rho</math>.<ref>Zaslow 2008, p.531</ref>
+===T-duality===
+[[File:torus cycles.png|thumb|right|A torus is the product of two circles, in this case the red circle is swept around axis defining the pink circle. <math>R_1</math> is the radius of the red circle, <math>R_2</math> is the radius of the pink one.]]
+{{main|T-duality}}
+We have now seen how a torus can be obtained by identifying opposite sides of a parallelogram in the complex plane. A particularly simple example is where the complex numbers <math>\omega_1</math> and <math>\omega_2</math> lie on the real and imaginary axes, respectively. In this case, we can write <math>\omega_1=R_1</math> and <math>\omega_2=iR_2</math> where <math>R_1</math> and <math>R_2</math> are real numbers. As discussed above, the complex structure on the torus obtained in this way is characterized by the number <math>\tau=iR_2/R_1</math>.
+We have explained how the symplectic structure of the torus is determined by an area element. We can choose coordinates <math>x</math> and <math>y</math> on our parallelogram so that each side of the parallelogram spanned by the chosen complex numbers has length 1. Then the area element of our torus is <math>R_1R_2dxdy</math> which integrates to <math>R_1R_2</math> on the unit square. We define the symplectic parameter <math>\rho</math> to be the product <math>iR_1R_2</math>.
+Note that the torus can also be considered as a [[cartesian product]] of two circles. This means that at each point of an equatorial circle on the torus (illustrated in pink), there is a longitudinal circle (illustrated in red).
+Let us now imagine that the torus represents the "spacetime" for a [[physical theory]]. The fundamental objects of this theory will be [[string (physics)|strings]] propagating through the spacetime according to the rules of [[quantum mechanics]]. One of the basic [[duality (physics)|dualities]] of [[string theory]] is [[T-duality]], which states that a string propagating around a circle of radius <math>R</math> is equivalent to a string propagating around a circle of radius <math>1/R</math> in the sense that all observable quantities in one description are identified with quantities in the dual description.<ref>Zaslow 2008, p.532</ref> For example, the [[momentum]] of a string in one description takes discrete values and is equal to the number of times the string [[winding number|winds]] around the circle in the dual description.<ref>Zaslow 2008, p.532</ref> Applying T-duality to the longitudinal circle on the torus, we find that there is an equivalent description in which spacetime is represented by a different torus. The duality changes <math>R_1</math> to <math>1/R_1</math>, and thus it interchanges the complex and symplectic parameters:
+: <math>\tau\leftrightarrow\rho</math>.
+In general, mirror symmetry is an equivalence of two physical theories that translates problems in [[complex geometry]] into problems in [[symplectic geometry]]. The torus considered here is the only [[compact topological space|compact]] Calabi-Yau manifold of (real) dimension two and is therefore the simplest example of mirror symmetry.<ref>Zaslow 2008, p.533</ref> In applications to string theory, one usually considers a six-dimensional Calabi-Yau manifold, where the six dimensions correspond to the six unobserved dimensions of spacetime.
+==Applications of mirror symmetry==
+===Enumerative geometry===
+{{main|Enumerative geometry}}
+[[File:Apollonius8ColorMultiplyV2.svg|thumb|right|[[Problem of Apollonius|Circles of Apollonius]].]]
+Many of the important mathematical applications of mirror symmetry belong to the branch of mathematics called [[enumerative geometry]]. In enumerative geometry, one is interested in counting the number of solutions to geometric questions, typically using the techniques of [[algebraic geometry]]. One of the earliest problems of enumerative geometry was posed around the year 200 [[BCE]] by the ancient Greek mathematician [[Apollonius of Perga|Apollonius]], who asked how many circles in the plane are tangent to three given circles.<ref>Yau and Nadis 2010, p.166</ref> In general, the solution to the [[problem of Apollonius]] is that there are eight such circles. The picture on the right shows an example where the three given circles are illustrated in black.
+[[File:Clebsch Cublic.png|thumb|left|The [[Clebsch cubic]].]]
+Enumerative problems in mathematics often concern a class of geometric objects called [[algebraic varieties]] which are defined by the vanishing of [[polynomial]]s. For example, the [[Clebsch cubic]] is the surface illustrated on the left which is defined using a certain polynomial of [[degree of a polynomial|degree]] three in four variables. A celebrated result of nineteenth-century mathematicians [[Arthur Cayley]] and [[George Salmon]] states that there are exactly 27 straight lines that lie entirely on such a surface.<ref>Yau and Nadis 2010, p.167</ref>
+Generalizing this problem, one can ask how many lines can be drawn on a quintic such as the Calabi-Yau illustrated above. This problem was solved by the nineteenth-century German mathematician [[Hermann Schubert]], who found that there are exactly 2,875 such lines. In 1986, geometer [[Sheldon Katz]] proved that the number of curves of degree two (such as circles) which lie entirely in the quintic is 609,250.<ref>Yau and Nadis 2010, p.166</ref>
+By the year 1991, most of the classical problems of enumerative geometry had been solved and interest in enumerative geometry had begun to diminish. According to mathematician [[Mark Gross]], "As the old problems had been solved, people went back to check Schubert's numbers with modern techniques, but that was getting pretty stale."<ref>Yau and Nadis 2010, p.169</ref> The field was reinvigorated in May 1991 when physicists [[Philip Candelas]], Xenia de la Ossa, Paul Green, and Linda Parks showed that mirror symmetry could be used to count the number of degree three curves lie on a quintic Calabi-Yau. Roughly speaking, one can think of such a degree three curve as a sphere that lies entirely inside the Calabi-Yau.<ref>Yau and Nadis 2010, p.168</ref> Candelas and his collaborators found that such these six-dimensional Calabi-Yau manifolds can contain exactly 317,206,375 curves of degree three.<ref>Yau and Nadis 2010, p.169</ref>
+In addition to counting degree-three curves on a quintic three-fold, Candelas and his collaborators obtained a number of more general results for counting rational curves which went far beyond the results obtained by mathematicians.<ref>Yau and Nadis 2010, p.171</ref> Although the methods used in this work were based on [[mathematical rigor|nonrigorous]] ideas from [[theoretical physics]], mathematicians have gone on to [[mathematical proof|rigorously prove]] some of the predictions of mirror symmetry. In particular, the enumerative predictions of mirror symmetry have now been rigorously proven.<ref>Yau and Nadis 2010, p.172</ref>
+===String theory===
+In addition to its applications to enumerative geometry, mirror symmetry is a fundamental tool for doing calculations in [[string theory]]. When a calculation in string theory is impossible using the techniques of [[perturbation theory]], theorists can apply dualities such as mirror symmetry to translate the calculation into an equivalent calculation in a ''different'' theory. By outsourcing calculations to different theories in this way, theorists can calculate many quantities that are impossible to calculate without the use of dualities.<ref>Zaslow 2008, sec. 10</ref>
+==Approaches to mirror symmetry==
+===Homological mirror symmetry===
+{{main|Homological mirror symmetry}}
+[[File:D3-brane et D2-brane.PNG|thumb|right|350px|Open strings attached to a pair of [[D-brane]]s.]]
+In [[string theory]] and related theories such as [[Supergravity|supergravity theories]], a ''brane'' is a physical object that generalizes the notion of a point particle to higher dimensions.<ref>Moore 2005, p.214</ref> For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher dimensional branes. The word brane comes from the word "membrane" which refers to a two-dimensional brane.
+In string theory, a [[string (physics)|string]] may be open (forming a segment with two endpoints) or closed (forming a closed loop). [[D-brane]]s are an important class of branes that arise when one considers open strings.<ref>Moore 2005, p.215</ref> As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to the fact that we impose a certain mathematical condition on the system known as the [[Dirichlet boundary condition]].
+Mathematically, branes can be described using the notion of a [[category (mathematics)|category]].<ref>Aspinwall et al. 2009</ref> This is a mathematical structure consisting of ''objects'', and for any pair of objects, a set of ''morphisms'' between them. In most examples, the objects are mathematical structures of some kind (for example, [[set (mathematics)|set]]s, [[vector spaces]], or [[topological spaces]]) and the morphisms are given by [[function (mathematics)|functions]] between these structures.<ref>A basic reference on category theory is Mac Lane 1998.</ref> We can also consider categories where the objects are D-branes and the morphisms between two branes <math>\alpha</math> and <math>\beta</math> are [[wavefunction]]s of open strings stretched between <math>\alpha</math> and <math>\beta</math>.<ref>Zaslow 2008, p.536</ref>
+In the B-model of [[topological string theory]], the category of D-branes is constructed from the [[complex geometry]] of the Calabi-Yau manifold on which the strings propagate. In mathematical language, it is known as the [[derived category]] of [[coherent sheaves]] on the Calabi-Yau. On the other hand, the category of D-branes in the A-model is constructed from the [[symplectic geometry]] of the mirror Calabi-Yau. It is known in mathematics as the [[Fukaya category]].<ref>Aspinwall et al. 2009, p.575</ref> The [[homological mirror symmetry]] conjecture of [[Maxim Kontsevich]] states that these two categories of branes are equivalent in a certain sense.<ref>Aspinwall et al. 2009, p.616</ref>
+===Strominger-Yau-Zaslow conjecture===
+{{main|SYZ conjecture}}
+Another approach to understanding mirror symmetry was suggested by [[Andrew Strominger]], [[Shing-Tung Yau]], and [[Eric Zaslow]] in 1996.<ref>Strominger, Yau, and Zaslow 1996</ref> According to the SYZ conjecture, mirror symmetry can be understood by dividing a complicated Calabi-Yau manifold into simpler pieces and considering the effects of [[T-duality]] on these pieces.<ref>Yau and Nadis 2010, p.174</ref>
+Recall that in the Overview section we considered the case of a [[torus]], and we viewed this torus as the [[cartesian product|product]] of two circles. This means that the torus can be viewed as the [[union (set theory)|union]] of a collection of longitudinal circles (such as the red circle in the image). There is an auxiliary space which says how these circles are organized, and this space is itself a circle (the pink circle). This space is said to ''parametrize'' the longitudinal circles on the torus. As explained above, mirror symmetry is equivalent to T-duality acting on the longitudinal circles, changing their radii from <math>R_1</math> to <math>1/R_1</math>.
+The SYZ conjecture generalizes this idea to the more complicated case of six-dimensional Calabi-Yau manifolds. As in the case of a torus, we can divide a six-dimensional Calabi-Yau into simpler pieces, which in this case are [[3-torus|3-tori]] (three-dimensional objects which generalize the notion of a torus) parametrized by a [[3-sphere]] (a three-dimensional generalization of a sphere).<ref>More precisely, there is a 3-torus associated to every point on the three-sphere except at certain bad points, which correspond to singular tori. See Yau and Nadis 2010, pp.176--7.</ref> T-duality can be extended from circles to the three-dimensional tori appearing in this decomposition, and the SYZ conjecture states that mirror symmetry is equivalent to the simultaneous application of T-duality to these three-dimensional tori.<ref>Yau and Nadis 2010, p.178</ref> In this way, the SYZ conjecture provides a geometric picture of how mirror symmetry acts on a Calabi-Yau manifold.
+==History==
+The idea of mirror symmetry can be traced back to the mid-1980s when it was noticed that a [[string (physics)|string]] propagating on a circle of radius <math>R</math> is physically equivalent to a string propagating on a circle of radius <math>1/R</math> in appropriate [[units of measurements|units]].<ref>This was first observed in Kikkawa and Yamasaki 1984 and Sakai and Senda 1986.</ref> This phenomenon is now known as [[T-duality]] and is understood to be closely related to mirror symmetry.
+In a paper from 1985, [[Philip Candelas]], [[Gary Horowitz]], [[Andrew Strominger]], and [[Edward Witten]] showed that by [[compactification (physics)|compactifying]] string theory on a [[Calabi-Yau manifold]], one obtains a theory roughly similar to the [[standard model of particle physics]].<ref>Candelas et al. 1985</ref> Following this development, many physicists began studying Calabi-Yau compactifications, hoping to construct realistic models of particle physics based on string theory. It was noticed that given such a physical model, it is not possible to uniquely reconstruct a corresponding Calabi-Yau manifold. Instead, one finds that there are ''two'' Calabi-Yau manifolds that give rise to the same physics.<ref>This was observed in Dixon 1988 and Lerche, Vafa, and Warner 1989.</ref>
+Mathematicians became interested in mirror symmetry around 1990 when physicists Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parks showed that mirror symmetry could be used to solve certain problems in [[enumerative geometry]], some of which had resisted solution for decades or more.<ref>Yau and Nadis 2010, p.165</ref> These results were presented to mathematicians at a conference at the [[Mathematical Sciences Research Institute]] (MSRI) in [[Berkeley, California]] in May 1991. During this conference, it was noticed that one of the numbers Candelas had computed for the problem of counting [[rational curve]]s disagreed with the number obtained by [[Norwegians|Norwegian]] mathematicians [[Geir Ellingsrud]] and [[Stein Arild Strømme]] using ostensibly more rigorous techniques.<ref>Yau and Nadis 2010, p.169--170</ref> Many mathematicians at the conference assumed that Candelas's work contained a mistake since it was not based on rigorous mathematical arguments. However, after examining their solution, Ellingsrud and Strømme discovered an error in their computer code and, upon fixing the code, they got an answer that agreed with the one obtained by Candelas and his collaborators.<ref>Yau and Nadis 2010, p.170</ref>
+In 1990, Edward Witten introduced [[topological string theory]],<ref>Witten 1990</ref> a simplified version of string theory, and physicists showed that there is a version of mirror symmetry for topological string theory.<ref>Vafa 1992; Witten 1992</ref> This statement about topological string theory is usually taken as the definition of mirror symmetry in the mathematical literature.<ref>Hori et al. 2003, p. xviii</ref> In an address at the [[International Congress of Mathematicians]] in 1994, mathematician [[Maxim Kontsevich]] presented a new mathematical conjecture based on the physical idea of mirror symmetry in topological string theory. Known as [[homological mirror symmetry]], this conjecture formalizes mirror symmetry as an equivalence of two mathematical structures: the [[derived category]] of [[coherent sheaf|coherent sheaves]] on a Calabi-Yau manifold and the [[Fukaya category]] of its mirror.<ref>Kontsevich 1995</ref>
+Also around 1995, Kontsevich analyzed the results of Candelas, which gave a general formula for the problem of counting [[rational curve]]s on a [[quintic threefold]], and he reformulated these results as a precise mathematical conjecture. In 1996, [[Alexander Givental]] posted a paper which claimed to prove this conjecture of Kontsevich.<ref>Givental 1996, 1998</ref> Initially, many mathematicians found this paper hard to understand, and so there were doubts about the correctness of Givental's proof. In the years following this, [[Bong Lian]], [[Kefeng Liu]], and [[Shing-Tung Yau]] published an independent proof in a series of papers.<ref>Lian, Liu, Yau 1997, 1999, 2000</ref> Despite some controversy over who had published the first proof, these papers are now seen as providing a mathematical proof of the results originally obtained by physicists using mirror symmetry.<ref>Yau and Nadis 2010, p.172</ref>
+==See also==
+* [[3D mirror symmetry]]
+* [[Chern-Simons theory]]
+* [[Donaldson-Thomas theory]]
+* [[Monstrous moonshine]]
+* [[Seiberg-Witten invariant]]
+* [[Vertex operator algebra]]
+* [[Wall-crossing]]
+==Notes==
+{{reflist|2}}
+==References==
+{{refbegin|2}}
+* {{cite book |editor1-first=Paul |editor1-last=Aspinwall |editor2-first=Tom |editor2-last=Bridgeland |editor3-first=Alastair |editor3-last=Craw |editor4-first=Michael |editor4-last=Douglas |editor5-first=Mark |editor5-last=Gross |editor6-first=Anton |editor6-last=Kapustin |editor7-first=Gregory |editor7-last=Moore |editor8-first=Graeme |editor8-last=Segal |editor9-first=Balázs |editor9-last=Szendröi |editor10-first=P.M.H. |editor10-last=Wilson |title=Dirichlet Branes and Mirror Symmetry |year=2009 |publisher=American Mathematical Society}}
+* {{cite journal |last1=Candelas |first1=Philip |last2=Horowitz |first2=Gary |last3=Strominger |first3= Andrew |last4=Witten |first4=Edward |year=1985 |title=Vacuum configurations for superstrings |journal=Nuclear Physics B |volume=258 |issue= |pages=46–74|bibcode = 1985NuPhB.258...46C |doi = 10.1016/0550-3213(85)90602-9 }}
+* {{cite journal |last1=Dixon |first1=Lance |year=1988 |title=Some world-sheet properties of superstring compactifications, on orbifolds and otherwise |journal=ICTP Ser. Theoret. Phys. |volume=4 |pages=67–126}}
+* {{cite journal |last1=Givental |first1=Alexander |year=1996 |title=Equivariant Gromov-Witten invariants |journal=International Mathematics Research Notices |volume=1996 |issue=13 |pages=613–663}}
+* {{cite journal |last1=Givental |first1=Alexander |year=1998 |title=A mirror theorem for toric complete intersections |journal=Topological field theory, primitive forms and related topics |pages=141–175}}
+* {{cite book |last1=Greene |first1=Brian |title=The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory |year=2000 |publisher=Random House }}
+* {{cite book |editor1-first=Kentaro |editor1-last=Hori |editor2-first=Sheldon |editor2-last=Katz |editor3-first=Albrecht |editor3-last=Klemm |editor4-first=Rahul |editor4-last=Pandharipande |editor5-first=Richard |editor5-last=Thomas |editor6-first=Cumrun |editor6-last=Vafa |editor7-first=Ravi |editor7-last=Vakil |editor8-first=Eric |editor8-last= Zaslow|title=Mirror Symmetry |year=2003 |publisher=American Mathematical Society|url=http://math.stanford.edu/~vakil/files/mirrorfinal.pdf|isbn=0821829556}}
+* {{cite journal |last1=Kikkawa |first1=Keiji |last2=Yamasaki |first2=Masami |year=1984 |title=Casimir effects in superstring theories |journal=Physics Letters B |volume=149 |issue=4 |pages=357–360|bibcode = 1984PhLB..149..357K |doi = 10.1016/0370-2693(84)90423-4 }}
+* {{cite journal |last1=Kontsevich |first1=Maxim |year=1995 |title=Homological algebra of mirror symmetry |journal=Proceedings of the International Congress of Mathematicians |pages=120–139}}
+* {{cite journal |last1=Lerche |first1=Wolfgang |last2=Vafa |first2=Cumrun |last3=Warner |first3=Nicholas |year=1989 |title=Chiral rings in <math>N = 2</math> superconformal theories |journal=Nuclear Physics B |volume=324 |issue=2 |pages=427–474|bibcode = 1989NuPhB.324..427L |doi = 10.1016/0550-3213(89)90474-4 }}
+* {{cite journal |last1=Lian |first1=Bong |last2=Liu |first2=Kefeng |last3=Yau |first3=Shing-Tung |year=1997 |title=Mirror principle, I |journal=Asian Journal of Math |volume=1 |pages=729–763}}
+* {{cite journal |last1=Lian |first1=Bong |last2=Liu |first2=Kefeng |last3=Yau |first3=Shing-Tung |year=1999 |title=Mirror principle, II |journal=Asian Journal of Math |volume=3 |pages=109–146}}
+* {{cite journal |last1=Lian |first1=Bong |last2=Liu |first2=Kefeng |last3=Yau |first3=Shing-Tung |year=1999 |title=Mirror principle, III |journal=Asian Journal of Math |volume=3 |pages=771–800}}
+* {{cite journal |last1=Lian |first1=Bong |last2=Liu |first2=Kefeng |last3=Yau |first3=Shing-Tung |year=2000 |title=Mirror principle, IV |journal=Surveys in Differential Geometry |pages=475–496}}
+* {{cite book |last1=Mac Lane |first1=Saunders |title=Categories for the Working Mathematician |year=1998}}
+* {{cite journal| author=Moore, Gregory | title=What is... a Brane?| journal=Notices of the AMS| year=2005 | url=http://www.ams.org/notices/200502/what-is.pdf |format=PDF| accessdate=June 2013 |page=214|  volume=52}}
+* {{cite journal |last1=Sakai |first1=Norisuke |last2=Senda |first2=Ikuo |year=1986 |title=Vacuum energies of string compactified on torus |journal=Progress of Theoretical Physics |volume=75 |issue=3 |pages=692–705|bibcode = 1986PThPh..75..692S |doi = 10.1143/PTP.75.692 }}
+* {{cite journal |last1=Strominger |first1=Andrew |last2=Yau |first2=Shing-Tung |last3=Zaslow |first3=Eric |year=1996 |title=Mirror symmetry is T-duality |journal=Nuclear Physics B |volume=479 |issue=1 |pages=243–259|arxiv = hep-th/9606040 |bibcode = 1996NuPhB.479..243S |doi = 10.1016/0550-3213(96)00434-8 }}
+* {{cite journal |last1=Vafa |first1=Cumrun |year=1992 |title=Topological mirrors and quantum rings |journal=Essays on mirror manifolds |pages=96–119}}
+* {{cite journal |last1=Witten |first1=Edward |year=1990 |title=On the structure of the topological phase of two-dimensional gravity |journal=Nuclear Physics B |volume=340 |pages=281–332|bibcode = 1990NuPhB.340..281W |doi = 10.1016/0550-3213(90)90449-N }}
+* {{cite journal |last1=Witten |first1=Edward |year=1992 |title=Mirror manifolds and topological field theory |journal=Essays on mirror manifolds |pages=121–160}}
+* {{Cite book| first1 = Shing-Tung | last1 = Yau | first2 = Steve | last2 = Nadis | year = 2010 | title = The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions | publisher = Basic Books | isbn = 978-0-465-02023-2 }}
+* {{Citation | last1=Zaslow | first1=Eric | contribution=Mirror Symmetry | year=2008 | title=The Princeton Companion to Mathematics | editor-last=Gowers | editor-first=Timothy}}
+* {{cite book |last1=Zwiebach |first1=Barton |title=A First Course in String Theory |year=2009 |publisher=Cambridge University Press}}
+{{refend}}
+==Further reading==
+===Popularizations===
+* {{Cite book| first1 = Shing-Tung | last1 = Yau | first2 = Steve | last2 = Nadis | year = 2010 | title = The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions | publisher = Basic Books | isbn = 978-0-465-02023-2 }}
+* {{cite web |url=http://www.claymath.org/library/senior_scholars/zaslow_physmatics.pdf |title=Physmatics |last1=Zaslow |first1=Eric |year=2005 |accessdate=September 11, 2013}}
+* {{Citation | last1=Zaslow | first1=Eric | contribution=Mirror Symmetry | year=2008 | title=The Princeton Companion to Mathematics | editor-last=Gowers | editor-first=Timothy}}
+===Textbooks===
+* {{cite book |editor1-first=Paul |editor1-last=Aspinwall |editor2-first=Tom |editor2-last=Bridgeland |editor3-first=Alastair |editor3-last=Craw |editor4-first=Michael |editor4-last=Douglas |editor5-first=Mark |editor5-last=Gross |editor6-first=Anton |editor6-last=Kapustin |editor7-first=Gregory |editor7-last=Moore |editor8-first=Graeme |editor8-last=Segal |editor9-first=Balázs |editor9-last=Szendröi |editor10-first=P.M.H. |editor10-last=Wilson |title=Dirichlet Branes and Mirror Symmetry |year=2009 |publisher=American Mathematical Society}}
+* {{cite book |editor1-first=Kentaro |editor1-last=Hori |editor2-first=Sheldon |editor2-last=Katz |editor3-first=Albrecht |editor3-last=Klemm |editor4-first=Rahul |editor4-last=Pandharipande |editor5-first=Richard |editor5-last=Thomas |editor6-first=Cumrun |editor6-last=Vafa |editor7-first=Ravi |editor7-last=Vakil |editor8-first=Eric |editor8-last= Zaslow|title=Mirror Symmetry |year=2003 |publisher=American Mathematical Society|url=http://math.stanford.edu/~vakil/files/mirrorfinal.pdf|isbn=0821829556}}
+{{Good article}}
+{{DEFAULTSORT:Mirror Symmetry (String Theory)}}
+[[Category:Algebraic geometry]]
+[[Category:String theory]]
+[[es:Simetría especular]]
+[[sv:Spegelsymmetri]]
+[[zh:镜像对称]]

Higgs mechanism: Difference between revisions

Revision as of 10:11, 1 February 2014

Overview

The idea of mirror symmetry

Complex geometry

Symplectic geometry

T-duality

Applications of mirror symmetry

Enumerative geometry

String theory

Approaches to mirror symmetry

Homological mirror symmetry

Strominger-Yau-Zaslow conjecture

History

See also

Notes

References

Further reading

Popularizations

Textbooks

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