Estimates for zero loci of Bernstein-Sato ideals

TL;DR

This paper provides bounds for the zero loci of Bernstein-Sato ideals, extending known results for Bernstein-Sato polynomials and connecting them with log-canonical thresholds and multiplier ideals.

Contribution

It generalizes upper bounds for Bernstein-Sato polynomial roots to multivariate Bernstein-Sato ideals and relates lower bounds to log-canonical thresholds and jumping numbers.

Findings

Established a multivariate upper bound for zero loci

Connected roots of Bernstein-Sato ideals with log-canonical thresholds

Extended known bounds from polynomials to ideals

Abstract

We give estimates for the zero loci of Bernstein-Sato ideals. An upper bound is proved as a multivariate generalisation of the upper bound by Lichtin for the roots of Bernstein-Sato polynomials. The lower bounds generalise the fact that log-canonical thresholds, small jumping numbers of multiplier ideals, and their real versions provide roots of Bernstein-Sato polynomials.