Torsion in Milnor fiber homology

Abstract

In a recent paper, Dimca and Némethi pose the problem of finding a homogeneous polynomial $f$ such that the homology of the complement of the hypersurface defined by $f$ is torsion-free, but the homology of the Milnor fiber of $f$ has torsion. We prove that this is indeed possible, and show by construction that, for each prime $p$, there is a polynomial with $p$–torsion in the homology of the Milnor fiber. The techniques make use of properties of characteristic varieties of hyperplane arrangements.