Bernstein-Sato polynomials and analytic non-equivalence of plane curve singularities

TL;DR

This paper investigates the Bernstein-Sato polynomials of plane curve singularities, showing that some topologically equivalent pairs are not analytically equivalent due to differences in their Bernstein-Sato polynomials.

Contribution

It computes Bernstein-Sato polynomials for specific pairs of plane curve singularities and demonstrates their effectiveness in distinguishing analytic types.

Findings

Some pairs with identical Tjurina numbers have different Bernstein-Sato polynomials.

Bernstein-Sato polynomials can detect non-analytic equivalence among topologically equivalent singularities.

Abstract

We compute Bernstein-Sato polynomials of some pairs of topologically equivalent plane curve singularities. Some pairs have the same Tjurina number but distinct Bernstein-Sato polynomials, which implies that they are not analytically equivalent.