The monodromy conjecture for hyperplane arrangements
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Publication:634719
DOI10.1007/S10711-010-9560-1zbMATH Open1227.32035arXiv0906.1991OpenAlexW2049221857MaRDI QIDQ634719
Author name not available (Why is that?)
Publication date: 16 August 2011
Published in: (Search for Journal in Brave)
Abstract: The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2pi i c) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture asserts that every pole 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 the affine n-space.
Full work available at URL: https://arxiv.org/abs/0906.1991
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