Multivariable Alexander invariants of hypersurface complements
Algebraic Topology
2012-04-03 v2 Algebraic Geometry
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 to the purity of some cohomology groups.
Cite
@article{arxiv.math/0506324,
title = {Multivariable Alexander invariants of hypersurface complements},
author = {Alexandru Dimca and Laurentiu Maxim},
journal= {arXiv preprint arXiv:math/0506324},
year = {2012}
}
Comments
In the second version new corollaries are added and some examples involving admissible local systems are clarified