Document Type

Article

Publication Date

8-1-2011

DOI

http://dx.doi.org/10.1007/s10711-010-9560-1

Abstract

The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2πic) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture asserts that every such c is a root of the Bernstein-Sato polynomial of the hypersurface. In this note we prove the weak version of the conjecture for hyperplane arrangements. Furthermore, we reduce the strong version to the following conjecture: −n/d is always a root of the Bernstein-Sato polynomial of an indecomposable essential central hyperplane arrangement of d hyperplanes in Cn.

Copyright Statement

This is an author-produced, peer-reviewed version of this article. The final publication is available at www.springerlink.com. Copyright restrictions may apply. DOI: 10.1007/s10711-010-9560-1

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