Torsion in Milnor fiber homology

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 2000

Primary: 32S55

Secondary: 14J70, 32S22, 55N25

References

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Publication

Received: 14 February 2003

Accepted: 19 May 2003

Published: 15 June 2003

Authors

Daniel C Cohen
Department of Mathematics Louisiana State University Baton Rouge LA 70803 USA

Graham Denham
Department of Mathematics University of Western Ontario London, ON N6A 5B7 Canada

Alexander I Suciu
Department of Mathematics Northeastern University Boston MA 02115 USA

Volume 3, issue 1 (2003)

Daniel C Cohen, Graham Denham and Alexander I Suciu