Multiplier ideals via Mather discrepancy

TL;DR

This paper introduces Mather multiplier ideals for varieties with arbitrary singularities, establishing key theorems like vanishing, restriction, subadditivity, and Skoda type results, and applying them to integral closure formulas.

Contribution

It defines Mather multiplier ideals using Mather discrepancy and Jacobian ideals, extending multiplier ideal theory to singular varieties with new vanishing and subadditivity theorems.

Findings

Proves a relative vanishing theorem for Mather multiplier ideals

Establishes restriction, subadditivity, and summation theorems

Derives a Briancon-Skoda type formula for integral closures

Abstract

We define a version of multiplier ideals, the Mather multiplier ideals, on a variety with arbitrary singularities, using the Mather discrepancy and the Jacobian ideal. In this context we prove a relative vanishing theorem, thus obtaining restriction theorems and a subadditivity and summation theorems. The Mather multiplier ideals also satisfy a Skoda type result. As an application, we obtain a Briancon-Skoda type formula for the integral closures of ideals on a variety with arbitrary singularities.