A short note on the multiplier ideals of monomial space curves

TL;DR

This paper simplifies the computation of multiplier ideals for monomial space curves by reducing the number of auxiliary valuations needed, using a more intrinsic, toric-based approach.

Contribution

It demonstrates that only one auxiliary valuation is necessary for the multiplier ideal formula, improving upon Thompson's previous multi-valuation method.

Findings

Reduction to a single auxiliary valuation simplifies calculations.

Uses a more intrinsic approach based on toric geometry.

Provides a streamlined method for computing multiplier ideals.

Abstract

Thompson (2014) exhibits a formula for the multiplier ideal with multiplier lambda of a monomial curve C with ideal I as an intersection of a term coming from the I-adic valuation, the multiplier ideal of the term ideal of I, and terms coming from certain specified auxiliary valuations. This short note shows it suffices to consider only one auxiliary valuation. This improvement is achieved through a more intrinsic approach, reduction to the toric case.