On the Tensor Property of Bernstein-Sato Polynomial

2024/06/06 by Shi, Quan, Zuo, Huaiqing · 1 citation
#13A35 #13N10 #14F10 #16S32 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.04121

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.

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