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<p><b>New page</b></p><div>In [[commutative algebra]], the '''multiplier ideal''' associated to a [[sheaf (mathematics)|sheaf]] of [[ideal (ring theory)|ideals]] over a [[complex number|complex]] [[algebraic variety|variety]] and a real number ''c'' consists (locally) of the functions ''h'' such that<br />
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: <math>\frac{|h|^2}{\sum|f_i^2|^c}</math><br />
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is [[locally integrable function|locally integrable]], where the ''f''<sub>''i''</sub> are a finite set of local generators of the ideal. Multiplier ideals were independently introduced by {{harvtxt|Nadel|1989}} (who worked with sheaves over complex manifolds rather than ideals) and {{harvtxt|Lipman|1993}}, who called them adjoint ideals.<br />
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Multiplier ideals are discussed in the survey articles {{harvtxt|Blickle|Lazarsfeld|2004}}, {{harvtxt|Siu|2005}}, and {{harvtxt|Lazarsfeld|2009}}.<br />
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==References==<br />
*{{Citation | last1=Blickle | first1=Manuel | last2=Lazarsfeld | first2=Robert | title=Trends in commutative algebra | url=http://www.msri.org/communications/books/Book51/contents.html | publisher=[[Cambridge University Press]] | series=Math. Sci. Res. Inst. Publ. | mr=2132649 | year=2004 | volume=51 | chapter=An informal introduction to multiplier ideals | pages=87–114}}<br />
*{{Citation | last1=Lazarsfeld | first1=Robert | title=A short course on multiplier ideals | arxiv=0901.0651 | year=2009 | journal=2008 PCMI lectures}}<br />
*{{Citation | last1=Lipman | first1=Joseph | title=Adjoints and polars of simple complete ideals in two-dimensional regular local rings | url=http://www.math.purdue.edu/~lipman/papers/polars.pdf | mr=1316244 | year=1993 | journal=Bulletin de la Société Mathématique de Belgique. Série A | volume=45 | issue=1 | pages=223–244}}<br />
*{{Citation | last1=Nadel | first1=Alan Michael | title=Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature | jstor=34630 | mr=1015491 | year=1989 | journal=[[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the United States of America]] | volume=86 | issue=19 | pages=7299–7300}}<br />
*{{Citation | last1=Siu | first1=Yum-Tong | title=Multiplier ideal sheaves in complex and algebraic geometry | doi=10.1007/BF02884693 | mr=2156488 | year=2005 | journal=Science China Mathematics | volume=48 | pages=1–31}}<br />
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[[Category:Commutative algebra]]</div>en>ShelfSkewed