Multiplier ideals of monomial space curves

TL;DR

This paper develops a formula for the multiplier ideals of monomial space curves using toric geometry, extending known results for monomial ideals by constructing a specific toric blowup for resolution.

Contribution

It introduces a method to compute multiplier ideals of monomial space curves via a toric blowup, providing a new approach to their resolution.

Findings

Derived a formula for multiplier ideals of monomial space curves

Constructed a toric blowup that yields a log resolution

Extended Howald's formula to space curves

Abstract

The goal of this paper is to produce a formula for the multiplier ideals of monomial space curves in the spirit of Howald's formula for the multiplier ideals of monomial ideals. This is achieved by constructing a toric blowup of affine space in such a way that a log resolution of the monomial curve may be constructed from this toric variety in a well controlled manner.