Bernstein-Sato polynomials for general ideals vs. principal ideals
Algebraic Geometry
2019-06-13 v2
Abstract
We show that given an ideal I generated by regular functions f_1,...,f_r on the smooth complex variety X, the Bernstein-Sato polynomial of I is equal to the reduced Bernstein-Sato polynomial of the function g=\sum_{i=1}^rf_iy_i on the product of X with an r-dimensional affine space. By combining this with results from [BMS], we relate invariants and properties of I to those of g. We also use the result on Bernstein-Sato polynomials to show that the Strong Monodromy Conjecture for Igusa zeta functions of principal ideals implies a similar statement for arbitrary ideals.
Cite
@article{arxiv.1906.03086,
title = {Bernstein-Sato polynomials for general ideals vs. principal ideals},
author = {Mircea Mustata},
journal= {arXiv preprint arXiv:1906.03086},
year = {2019}
}
Comments
7 pages; v.2: inaccuracy at the end of the proof of Theorem 1.4 corrected