Bernstein-Sato polynomial versus cohomology of the Milnor fiber for generic arrangements

Details Bernstein-Sato polynomial versus cohomology of the Milnor fiber for generic arrangements Bernstein-Sato polynomial versus cohomology of the Milnor fiber for generic arrangements

2002-04-07

arxiv.org/abs/math/0204080v3

Mathematics

Algebraic Geometry

27 pages, AMS latex, improved form, to appear in Compositio Math

Scientific paper

In this note we determine the Bernstein-Sato polynomial $b_Q(s)$ of a generic central arrangement $Q=\prod_{i=1}^kH_i$ of hyperplanes. We establish a connection between the roots of $b_Q(s)$ and the degrees of the generators for the top cohomology of the corresponding Milnor fiber. This connection holds for all homogeneous polynomials. We also introduce certain subschemes of the arrangement determined by the roots of $b_Q(s)$.

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