Bernstein-Sato ideals and hyperplane arrangements
Abstract
We study the relation between zero loci of Bernstein-Sato ideals and roots of b-functions and obtain a criterion to guarantee that roots of b-functions of a reducible polynomial are determined by the zero locus of the associated Bernstein-Sato ideal. Applying the criterion together with a result of Maisonobe we prove that the set of roots of the b-function of a free hyperplane arrangement is determined by its intersection lattice. We also study the zero loci of Bernstein-Sato ideals and the associated relative characteristic cycles for arbitrary central hyperplane arrangements. We prove the multivariable n/d conjecture of Budur for complete factorizations of arbitrary hyperplane arrangements, which in turn proves the strong monodromy conjecture for the associated multivariable topological zeta functions.
Keywords
Cite
@article{arxiv.2005.13502,
title = {Bernstein-Sato ideals and hyperplane arrangements},
author = {Lei Wu},
journal= {arXiv preprint arXiv:2005.13502},
year = {2020}
}