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arXiv · 1412.3607

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

Maria Alberich-Carramiñana·Josep Alvarez Montaner·Ferran Dachs-Cadefau·Víctor González-Alonso
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Abstract

We study the multiplicity of the jumping numbers of an $\mathfrak m$-primary ideal $\mathfrak a$ 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 $\mathfrak a$ proving, in particular, that it is a rational function.

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Maria Alberich-Carramiñana, Josep Alvarez Montaner, Ferran Dachs-Cadefau, Víctor González-Alonso. 2016-06-16. Poincaré series of multiplier ideals in two-dimensional local rings with rational singularities. https://arxiv.org/abs/1412.3607

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