On a Bernstein-Sato polynomial of a meromorphic function
Complex Variables
2023-05-08 v7 Algebraic Geometry
Abstract
We define Bernstein-Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara-Malgrange type theorem on their geometric monodromies, which would be useful also in relation with the monodromy conjecture. A new feature in the meromorphic setting is that we have several b-functions whose roots yield the same set of the eigenvalues of the Milnor monodromies. We introduce also multiplier ideal sheaves for meromorphic functions and show that their jumping numbers are related to our b-functions.
Cite
@article{arxiv.2110.15780,
title = {On a Bernstein-Sato polynomial of a meromorphic function},
author = {Kiyoshi Takeuchi},
journal= {arXiv preprint arXiv:2110.15780},
year = {2023}
}
Comments
21 pages, to appear in Nagoya Math. Journal