Constancy regions of mixed multiplier ideals in two-dimensional local rings with rational singularities

TL;DR

This paper investigates the structure of mixed multiplier ideals in two-dimensional local rings with rational singularities, providing an algorithm to compute constancy regions and analyze their properties.

Contribution

It introduces a method to determine the regions where mixed multiplier ideals are constant and offers an algorithm for their computation in specific ranges.

Findings

Characterization of jumping walls for mixed multiplier ideals

Algorithm for computing constancy regions

Insights into the structure of mixed multiplier ideals in rational singularities

Abstract

The aim of this paper is to study mixed multiplier ideals associated to a tuple of ideals in a two-dimensional local ring with a rational singularity. We are interested in the partition of the real positive orthant given by the regions where the mixed multiplier ideals are constant. In particular we reveal which information encoded in a mixed multiplier ideal determines its corresponding jumping wall and we provide an algorithm to compute all the constancy regions, and their corresponding mixed multiplier ideals, in any desired range.