Log canonical threshold and diagonal ideals

TL;DR

This paper characterizes certain finite colength ideals in local rings using log canonical thresholds and mixed multiplicities, inspired by an inequality from Demailly and Pham.

Contribution

It provides a new characterization of ideals with integral closure equal to monomial-generated ideals based on log canonical thresholds and mixed multiplicities.

Findings

Characterization of ideals via log canonical threshold and mixed multiplicities.

Connection between integral closure of ideals and monomial ideals.

Motivated by an inequality from Demailly and Pham.

Abstract

We characterize the ideals $I$ of $\mathcal O_n$ of finite colength whose integral closure is equal to the integral closure of an ideal generated by pure monomials. This characterization, which is motivated by an inequality proven by Demailly and Pham, is given in terms of the log canonical threshold of $I$ and the sequence of mixed multiplicities of $I$.