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UID:968@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20151203T140000
DTEND;TZID=Europe/Paris:20151203T150000
DTSTAMP:20151118T130000Z
URL:https://www.i2m.univ-amu.fr/evenements/multiplier-ideals-and-jumping-n
 umbers/
SUMMARY: (...): Multiplier ideals and jumping numbers
DESCRIPTION:: Multiplier ideals and jumping numbers are invariants that enc
 ode relevant information about the structure of the ideal to which they ar
 e associated. In general\, jumping numbers and multiplier ideals of a fixe
 d ideal are determined by the divisors appearing in the resolution of the 
 ideal. The main goal of this talk is to present some results for computing
  jumping numbers and other invariants related to it like the multiplicitie
 s and the Poincaré series.This talk will be divided in two parts\, corres
 ponding to the two-dimesional case and the higher dimensional case. The fi
 rst part will be devoted to present a formula to compute the multiplicity 
 of jumping numbers of an m-primary ideal in a 2-dimensional local ring wit
 h rational singularities. This formula leads to a simple way to detect whe
 ther a given rational number is a jumping number. Another consequence of t
 he formula is that it allows us to give an explicit rational expression fo
 r the Poincaré series of the multiplier ideals introduced by Galindo and 
 Monserrat in 2010. This Poincaré series encodes in a unified way the jump
 ing numbers and its corresponding multiplicities. This part is a joint wor
 k with Maria Alberich Carraminana\, Josep Àlvarez Montaner and Victor Gon
 zalez Alonso. The last part will be devoted to introduce some results in t
 he higher-dimensional case. This part is a joint work with Hans Baumers. R
 eferences: M. Alberich-Carraminana\, J. Àlvarez-Montaner and F. Dachs-Cad
 efau\, Multiplier ideals in two-dimensional local rings with rational sing
 ularities\, arXiv:1412.3605M. Alberich-Carraminana\, J. Àlvarez-Montaner\
 , F. Dachs-Cadefau and V. Gonzalez-Alonso\, Poincaré series of multiplier
  ideals in two-dimensional local rings with rational singularities\, arXiv
 :1412.3607https://perswww.kuleuven.be/~u0099663/
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DTSTART:20151025T020000
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