Poincaré series of multiplier ideals in two-dimensional local rings with rational singularities
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2014
- DOI:
- arXiv:
- arXiv:1412.3607
- Bibcode:
- 2014arXiv1412.3607A
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Commutative Algebra
- E-Print:
- 21 pages