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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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
  • MR Author ID: 58125
  • 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
  • Received by editor(s): August 25, 2005
  • Published electronically: February 21, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2299465