Torsion in Milnor fiber homology

Cohen, Daniel C¹ ; Denham, Graham² ; Suciu, Alexander I³

¹Department of Mathematics, Louisiana State University, Baton Rouge LA 70803, USA
²Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
³Department of Mathematics, Northeastern University, Boston MA 02115, USA

Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 511-535

Résumé

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.

Détail

DOI : 10.2140/agt.2003.3.511

Keywords: Milnor fibration, characteristic variety, arrangement

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