English

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.

Keywords

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

R2 v1 2026-06-22T07:27:39.214Z