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Geometriae Dedicata

, Volume 153, Issue 1, pp 131–137 | Cite as

The Monodromy Conjecture for hyperplane arrangements

  • Nero Budur
  • Mircea Mustaţă
  • Zach Teitler
Original Paper

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 .

Keywords

Monodromy Conjecture Hyperplane arrangements 

Mathematics Subject Classification (2000)

32S40 32S22 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA
  3. 3.Department of MathematicsBoise State UniversityBoiseUSA

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