The Monodromy Conjecture for hyperplane arrangements

2009/06/10 by Budur, Nero, Mustata, Mircea, Teitler, Zach · 1 citation
#32S22 #32S40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0906.1991

Abstract

The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2πi 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.

Cited by

• Birational zeta functions

Related

• TheN/D-Conjecture for Nonresonant Hyperplane Arrangements
• Computing Milnor fiber monodromy for some projective hypersurfaces
• Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements
• Bernstein-Sato ideals and hyperplane arrangements
• Bernstein-Sato polynomial versus cohomology of the Milnor fiber for generic arrangements