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 C n.
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The first author was partially supported by the NSF grant DMS-0700360, and the second author was partially supported by NSF grant DMS-0758454 and by a Packard Fellowship.
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Budur, N., Mustaţă, M. & Teitler, Z. The Monodromy Conjecture for hyperplane arrangements. Geom Dedicata 153, 131–137 (2011). https://doi.org/10.1007/s10711-010-9560-1
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DOI: https://doi.org/10.1007/s10711-010-9560-1