Poincaré series of multiplier ideals in two-dimensional local rings with rational singularities

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• 作者：Maria Alberich-Carramiñ ; ana^a ; ^{Maria.Alberich@upc.edu" class="auth_mail" title="E-mail the corresponding author} ; Josep À ; lvarez Montaner^a ; ^{Josep.Alvarez@upc.edu" class="auth_mail" title="E-mail the corresponding author} ; Ferran Dachs-Cadefau^b ; ^{Ferran.DachsCadefau@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Ví ; ctor Gonzá ; lez-Alonso^c ; ^{gonzalez@math.uni-hannover.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multiplier ideals ; Rational singularity
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：2 January 2017
• 年：2017
• 卷：304
• 期：Complete
• 页码：769-792
• 全文大小：457 K

文摘

We study the multiplicity of the jumping numbers of an class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816311793&_mathId=si1.gif&_user=111111111&_pii=S0001870816311793&_rdoc=1&_issn=00018708&md5=6c59e22d087586c60efc5bedcc053ae4" title="Click to view the MathML source">mclass="mathContainer hidden">class="mathCode">$\mathfrak{m}$-primary ideal class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816311793&_mathId=si2.gif&_user=111111111&_pii=S0001870816311793&_rdoc=1&_issn=00018708&md5=1978e5d09540b418fc36d767ae8a47a7" title="Click to view the MathML source">aclass="mathContainer hidden">class="mathCode">$\mathfrak{a}$ in a two-dimensional local ring with a rational singularity. The formula we provide for the multiplicities leads to a very simple and efficient method to detect whether a given rational number is a jumping number. We also give an explicit description of the Poincaré series of multiplier ideals associated to class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816311793&_mathId=si2.gif&_user=111111111&_pii=S0001870816311793&_rdoc=1&_issn=00018708&md5=1978e5d09540b418fc36d767ae8a47a7" title="Click to view the MathML source">aclass="mathContainer hidden">class="mathCode">$\mathfrak{a}$ proving, in particular, that it is a rational function.