Alexander polynomials: Essential variables and multiplicities
| dc.creator | Dimca, Alexandru | |
| dc.creator | Papadima, Stefan | |
| dc.creator | Suciu, Alexander I. | |
| dc.date | 2007-06-17 | |
| dc.date.accessioned | 2026-07-07T08:56:20Z | |
| dc.date.available | 2026-07-07T08:56:20Z | |
| dc.description | 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. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0706.2499 | |
| dc.identifier | http://arxiv.org/abs/0706.2499 | |
| dc.identifier | International Mathematics Research Notices (2008) Vol. 2008: article ID rnm119, 36 pages | |
| dc.identifier | doi:10.1093/imrn/rnm119 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146576 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 14F35, 20F34; 14M12, 55N25, 57M05, 57M25 | |
| dc.title | Alexander polynomials: Essential variables and multiplicities | |
| dc.type | text |