Bernstein-Sato polynomials for maximal minors and sub-maximal Pfaffians

TL;DR

This paper computes Bernstein-Sato polynomials for ideals generated by maximal minors and sub-maximal Pfaffians, confirming the Strong Monodromy Conjecture for these cases, advancing understanding in algebraic geometry and singularity theory.

Contribution

It explicitly determines Bernstein-Sato polynomials for these ideals and proves the Strong Monodromy Conjecture in these contexts, which was previously unresolved.

Findings

Bernstein-Sato polynomials are explicitly computed for maximal minors and sub-maximal Pfaffians.

The Strong Monodromy Conjecture is verified for these algebraic ideals.

Results contribute to the understanding of singularities in algebraic geometry.

Abstract

We determine the Bernstein-Sato polynomials for the ideal of maximal minors of a generic m x n matrix, as well as for that of sub-maximal Pfaffians of a generic skew-symmetric matrix of odd size. As a corollary, we obtain that the Strong Monodromy Conjecture holds in these two cases.