On the Tensor Property of Bernstein-Sato Polynomial

Abstract

We prove the multiplicative Thom-Sebastiani rule for Bernstein-Sato polynomials, answering the longstanding questions of Budur and Popa. We generalize the result to the tensor of two effective divisors on the product of two arbitrary non-singular complex varieties. This also leads to a multiplicative property related to Igusa's strong monodromy conjecture. Moreover, we propose an extension of our result to Bernstein-Sato polynomials for ideals and prove it for monomial ideals.

This is a paper finished at the beginning of January 2024. It was submitted to a journal on January 31, a week before the appearance of arXiv:2402.04512v2, which has some overlaps. Solutions in two papers are independent