Autori: A. Dimca, S. Papadima, A.I. Suciu

Editorial: International Mathematics Research Notices, article ID rnm119, 36 pages, 2008.

Rezumat:

We explore the codimension-one strata in the degree-one cohomology jumping loci of a finitely generated group, through the prism of the multivariable Alexander polynomial. As an application, we give new criteria that must be satisfied by fundamental groups of smooth, quasi-projective complex varieties. These criteria establish precisely which fundamental groups of boundary manifolds of complex line arrangements are quasi-projective. We also give sharp upper bounds for the twisted Betti ranks of a group, in terms of multiplicities constructed from the Alexander polynomial. For Seifert links in homology 3-spheres, these bounds become equalities, and our formula shows explicitly how the Alexander polynomial determines all the characteristic varieties.

Cuvinte cheie: characteristic varieties, Alexander polynomial, almost principal ideal, multiplicity, twisted Betti number, quasi-projective group, boundary manifold, Seifert link

URL: http://dx.doi.org/10.1093/imrn/rnm119