arXiv math/05063242005-06math.ATmath.AG

Multivariable Alexander invariants of hypersurface complements

Alexandru Dimca, Laurentiu Maxim

备注：: In the second version new corollaries are added and some examples involving admissible local systems are clarified
发表信息：: Trans. Amer. Math. Soc. 359 (2007), no. 7, 3505-3528

英文摘要：

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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