Year: 2026
Type: preprint
Abstract: We study roots of Bernstein-Sato polynomials of ideals. Our first main result gives a general partial differential equation criterion for detecting roots of the Bernstein-Sato polynomial of an ideal. For homogeneous case, we recast this criterion as an analytic condition, connecting the algebraic problem of locating roots with analytic properties of the defining data. As an application, we give a series of roots for the general determinantal ideal prove the strong monodromy conjecture for them. Keywords. Bernstein-Sato polynomial, determinantal variety, monodromy conjecture.
Source: arXiv (Cornell University)
Authors: Chen, Yifan, Zuo, Huaiqing
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221765668