Date(s) - 03/12/2015
14 h 00 min - 15 h 00 min
Catégories Pas de Catégories
Multiplier ideals and jumping numbers are invariants that encode 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 ideal. The main goal of this talk is to present some results for computing jumping numbers and other invariants related to it like the multiplicities and the Poincaré series.
This talk will be divided in two parts, corresponding to the two-dimesional case and the higher dimensional case. The first 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 whether 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 Monserrat in 2010. This Poincaré series encodes in a unified way the jumping numbers and its corresponding multiplicities. This part is a joint work with Maria Alberich Carraminana, Josep Àlvarez Montaner and Victor Gonzalez 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.
M. Alberich-Carraminana, J. Àlvarez-Montaner and F. Dachs-Cadefau, Multiplier ideals in two-dimensional local rings with rational singularities, arXiv:1412.3605
M. 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:1412.3607