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Multivariable Alexander invariants of hypersurface complements


Authors: Alexandru Dimca and Laurentiu Maxim
Journal: Trans. Amer. Math. Soc. 359 (2007), 3505-3528
MSC (2000): Primary 32S20, 32S22, 32S35, 32S60; Secondary 14J70, 14F17, 14F45
DOI: https://doi.org/10.1090/S0002-9947-07-04241-9
Published electronically: 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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Additional Information

Alexandru Dimca
Affiliation: Laboratoire J.A. Dieudonné, UMR du CNRS 6621, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France
Email: dimca@math.unice.fr

Laurentiu Maxim
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania
Address at time of publication: Department of Mathematics, University of Illinois at Chicago, 851 S Morgan Street, Chicago, Illinois, 60607
Email: lmaxim@math.uic.edu

DOI: https://doi.org/10.1090/S0002-9947-07-04241-9
Received by editor(s): August 25, 2005
Published electronically: February 21, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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