Bernstein-Sato Polynomials on Normal Toric Varieties

TL;DR

This paper extends Bernstein-Sato polynomials to ideals in normal semigroup rings, linking roots to multiplier ideal jumping coefficients and providing a new combinatorial description for these ideals.

Contribution

It generalizes Bernstein-Sato polynomials to a broader class of rings and relates roots to multiplier ideal invariants, with a new combinatorial approach.

Findings

Bernstein-Sato polynomials are extended to normal semigroup rings.

Roots of Bernstein-Sato polynomials relate to multiplier ideal jumping coefficients.

A new combinatorial description for multiplier ideals of monomial ideals is provided.

Abstract

We generalize the Bernstein-Sato polynomials of Budur, Mustata and Saito to ideals in normal semigroup rings. In the case of monomial ideals, we also relate the roots of the Bernstein-Sato polynomial to the jumping coefficients of the corresponding multiplier ideals. In order to prove the latter result, we obtain a new combinatorial description for the multiplier ideals of a monomial ideal in a normal semigroup ring.