Torsion in Milnor fiber homology

Details Torsion in Milnor fiber homology Torsion in Milnor fiber homology

2003-02-12

arxiv.org/abs/math/0302143v2

Algebr. Geom. Topol. 3 (2003), 511-535

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-16.abs.html

Scientific paper

10.2140/agt.2003.3.511

In a recent paper, Dimca and Nemethi 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.

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