Multivariable Alexander invariants of hypersurface complements

Dimca, Alexandru; Maxim, Laurentiu

doi:10.1090/S0002-9947-07-04241-9

Multivariable Alexander invariants of hypersurface complements
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by Alexandru Dimca and Laurentiu Maxim PDF

Trans. Amer. Math. Soc. 359 (2007), 3505-3528 Request permission

Abstract:

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 with the purity of some cohomology groups.

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