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ISSN 1088-6850(e) ISSN 0002-9947(p)

Multivariable Alexander invariants of hypersurface complements

Author(s): Alexandru Dimca; Laurentiu Maxim
Journal: Trans. Amer. Math. Soc. 359 (2007), 3505-3528.
MSC (2000): Primary 32S20, 32S22, 32S35, 32S60; Secondary 14J70, 14F17, 14F45
Posted: February 21, 2007
MathSciNet review: 2299465
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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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