Multiplier ideals in two-dimensional local rings with rational singularities
Algebraic Geometry
2016-05-05 v2 Commutative Algebra
Abstract
The aim of this paper is to study jumping numbers and multiplier ideals of any ideal in a two-dimensional local ring with a rational singularity. In particular we reveal which information encoded in a multiplier ideal determines the next jumping number. This leads to an algorithm to compute sequentially the jumping numbers and the whole chain of multiplier ideals in any desired range. As a consequence of our method we develop the notion of jumping divisor that allows to describe the jump between two consecutive multiplier ideals. In particular we find a unique minimal jumping divisor that is studied extensively.
Cite
@article{arxiv.1412.3605,
title = {Multiplier ideals in two-dimensional local rings with rational singularities},
author = {Maria Alberich-Carramiñana and Josep Alvarez Montaner and Ferran Dachs-Cadefau},
journal= {arXiv preprint arXiv:1412.3605},
year = {2016}
}
Comments
32 pages. To appear in Mich. Math. J