Multiplier ideals of meromorphic functions in dimension two

TL;DR

This paper introduces an effective computational method for multiplier ideals of meromorphic functions in two dimensions and proves that their jumping numbers become integers beyond a certain threshold.

Contribution

It presents a new practical approach for computing multiplier ideals and establishes a threshold beyond which all jumping numbers are integers.

Findings

Effective method for computing multiplier ideals

Meromorphic functions have integer jumping numbers after a threshold

Provides theoretical insights into the structure of jumping numbers

Abstract

We provide an effective method to compute multiplier ideals of meromorphic functions in dimension two. We also prove that meromorphic functions only have integer jumping numbers after reaching some threshold.