Multivariable Alexander invariants of hypersurface complements

Details Multivariable Alexander invariants of hypersurface complements Multivariable Alexander invariants of hypersurface complements

2005-06-16

arxiv.org/abs/math/0506324v2

Trans. Amer. Math. Soc. 359 (2007), no. 7, 3505-3528

Mathematics

Algebraic Topology

In the second version new corollaries are added and some examples involving admissible local systems are clarified

Scientific paper

We start with a discussion on Alexander invariants, and then prove some general results concerning the divisibility of the Alexander polynomials and the supports of the Alexander modules, via Artin's vanishing theorem for perverse sheaves. We conclude with explicit computations of twisted cohomology following an idea already exploited in the hyperplane arrangement case, which combines the degeneration of the Hodge to de Rham spectral sequence to the purity of some cohomology groups.

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