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

Abstract

In this note we determine the Bernstein-Sato polynomial $b_Q(s)$ of a generic central arrangement $Q={\prod }_{i=1}^k{H}_i$ 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 $b_Q(s)$.

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