Algebraic & Geometric Topology 3 (2003) 511–535

DOI: 10.2140/agt.2003.3.511

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.

Keywords

Milnor fibration, characteristic variety, arrangement

Mathematical Subject Classification

Primary: 32S55

Secondary: 14J70, 32S22, 55N25

References

Publication

Received: 14 February 2003
Accepted: 19 May 2003
Published: 15 June 2003

Authors