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UID:3911@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20151203T140000
DTEND;TZID=Europe/Paris:20151203T150000
DTSTAMP:20151118T130000Z
URL:https://www.i2m.univ-amu.fr/events/multiplier-ideals-and-jumping-numbe
rs/
SUMMARY:Multiplier ideals and jumping numbers -
DESCRIPTION:Multiplier ideals and jumping numbers are invariants that encod
e relevant information about the structure of the ideal to which they are
associated. In general\, jumping numbers and multiplier ideals of a fixed
ideal are determined by the divisors appearing in the resolution of the id
eal. The main goal of this talk is to present some results for computing j
umping numbers and other invariants related to it like the multiplicities
and the Poincaré series.This talk will be divided in two parts\, correspo
nding to the two-dimesional case and the higher dimensional case. The firs
t 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 with
rational singularities. This formula leads to a simple way to detect wheth
er a given rational number is a jumping number. Another consequence of the
formula is that it allows us to give an explicit rational expression for
the Poincaré series of the multiplier ideals introduced by Galindo and Mo
nserrat in 2010. This Poincaré series encodes in a unified way the jumpin
g numbers and its corresponding multiplicities. This part is a joint work
with Maria Alberich Carraminana\, Josep Àlvarez Montaner and Victor Gonza
lez Alonso. The last part will be devoted to introduce some results in the
higher-dimensional case. This part is a joint work with Hans Baumers. Ref
erences: M. Alberich-Carraminana\, J. Àlvarez-Montaner and F. Dachs-Cadef
au\, Multiplier ideals in two-dimensional local rings with rational singul
arities\, arXiv:1412.3605M. Alberich-Carraminana\, J. Àlvarez-Montaner\,
F. Dachs-Cadefau and V. Gonzalez-Alonso\, Poincaré series of multiplier i
deals in two-dimensional local rings with rational singularities\, arXiv:1
412.3607https://perswww.kuleuven.be/~u0099663/
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DTSTART:20151025T020000
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