Publication

Multiplier ideals in two-dimensional local rings with rational singularities

Journal Article (2016)

Journal

Michigan Mathematical Journal

Pages

287-320

Volume

65

Number

2

Doc link

http://dx.doi.org/10.1307/mmj/1465329014

File

Download the digital copy of the doc pdf document

Authors

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.

Categories

pattern recognition.

Author keywords

Multiplier ideals, jumping numbers, rational surface singularity

Scientific reference

M. Alberich-Carramiñana, F. Dachs and J. Àlvarez. Multiplier ideals in two-dimensional local rings with rational singularities. Michigan Mathematical Journal, 65(2): 287-320, 2016.