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| | {{BLP sources|date=January 2013}} |
| | '''Lothar Göttsche''' (born January 21, 1961 in [[Sønderborg Municipality|Sonderburg]], [[Denmark]]) is a [[Germans|German]] [[mathematician]], known for his work in [[algebraic geometry]]. After studying mathematics at the [[University of Kiel]], he received his [[Dr. rer. nat.]] under the direction of [[Friedrich Hirzebruch]] at the [[University of Bonn]] in 1989. He was invited as speaker to the [[International Congress of Mathematicians]] in [[Beijing]] in 2002. Göttsche is a research scientist at the [[International Centre for Theoretical Physics]] in [[Trieste]], [[Italy]]. He is also editor for [[Geometry & Topology]]. |
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| | Göttsche received international acclaim with his formula for the [[generating function]] for the [[Betti numbers]] of the [[Hilbert scheme]] of points on an algebraic [[surface]]: |
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| | If <math>S</math> is a smooth surface over an algebraically closed field of characteristic <math>0</math>, then the generating function for the motives of the Hilbert schemes of <math>S</math> can be expressed in terms of the [[motivic zeta function]] by Göttsche's formula |
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| | :<math>\sum_{n=0}^\infty[S^{[n]}]t^n=\prod_{m=1}^\infty Z(S,{\Bbb L}^{m-1}t^m)</math> |
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| | Here <math>S^{[n]}</math> is the Hilbert scheme of length <math>n</math> subschemes of <math>S</math>. |
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| | Göttsche is also the author of a celebrated conjecture predicting the number of [[curve]]s in certain [[Linear system of divisors|linear systems]] on algebraic [[Algebraic surfaces|surfaces]]. |
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| | In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-19.</ref> |
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| | ==References== |
| | {{reflist}} |
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| | ==External links== |
| | *[http://users.ictp.it/~gottsche/ Home page of Lothar Göttsche] |
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| | {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. --> |
| | | NAME =Gottsche, Lothar |
| | | ALTERNATIVE NAMES = |
| | | SHORT DESCRIPTION = German mathematician |
| | | DATE OF BIRTH = January 21, 1961 |
| | | PLACE OF BIRTH = |
| | | DATE OF DEATH = |
| | | PLACE OF DEATH = |
| | }} |
| | {{DEFAULTSORT:Gottsche, Lothar}} |
| | [[Category:German mathematicians]] |
| | [[Category:Algebraic geometers]] |
| | [[Category:People from Sønderborg Municipality]] |
| | [[Category:University of Kiel alumni]] |
| | [[Category:University of Bonn alumni]] |
| | [[Category:Fellows of the American Mathematical Society]] |
| | [[Category:1961 births]] |
| | [[Category:Living people]] |
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| | {{Germany-mathematician-stub}} |
Template:BLP sources
Lothar Göttsche (born January 21, 1961 in Sonderburg, Denmark) is a German mathematician, known for his work in algebraic geometry. After studying mathematics at the University of Kiel, he received his Dr. rer. nat. under the direction of Friedrich Hirzebruch at the University of Bonn in 1989. He was invited as speaker to the International Congress of Mathematicians in Beijing in 2002. Göttsche is a research scientist at the International Centre for Theoretical Physics in Trieste, Italy. He is also editor for Geometry & Topology.
Göttsche received international acclaim with his formula for the generating function for the Betti numbers of the Hilbert scheme of points on an algebraic surface:
If 
is a smooth surface over an algebraically closed field of characteristic 
, then the generating function for the motives of the Hilbert schemes of can be expressed in terms of the motivic zeta function by Göttsche's formula
![{\displaystyle \sum _{n=0}^{\infty }[S^{[n]}]t^{n}=\prod _{m=1}^{\infty }Z(S,{\mathbb {L}}^{m-1}t^{m})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac41e1c3ee51b12adbe350c8e81fb438b4f3cf0b)
Here ![{\displaystyle S^{[n]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/917f4afaaa791a189f7f0c52d694f4a3f9567c3e)
is the Hilbert scheme of length 
subschemes of .
Göttsche is also the author of a celebrated conjecture predicting the number of curves in certain linear systems on algebraic surfaces.
In 2012 he became a fellow of the American Mathematical Society.[1]
References
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External links
Template:Persondata
Template:Germany-mathematician-stub