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Zero loci of Bernstein-Sato ideals

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arxiv 1907.04010 v3 pith:MG53WU7S submitted 2019-07-09 math.AG

Nero Budur , Robin van der Veer , Lei Wu , Peng Zhou This is my paper · ORCID
classification math.AG
keywords bernstein-satocohomologylocimultivariaterelatingauthorb-functionclassical
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We prove a conjecture of the first author relating the Bernstein-Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. This generalizes a classical theorem of Malgrange and Kashiwara relating the b-function of a multivariate polynomial with the monodromy eigenvalues on the Milnor fibers cohomology.

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  1. Combinatorially Determined Zeroes of Bernstein--Sato Ideals for Tame and Free Arrangements

    math.AG 2019-09 accept novelty 7.0 of 10

    For tame and free hyperplane arrangements, the zero loci of Bernstein-Sato ideals and the roots in [-1,0) of Bernstein-Sato polynomials are determined by the intersection lattice, with explicit combinatorial formulas.

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