Characteristic varieties of arrangements
| dc.creator | Cohen, Daniel C. | |
| dc.creator | Suciu, Alexander I. | |
| dc.date | 1998-01-11 | |
| dc.date | 1998-04-11 | |
| dc.date.accessioned | 2026-07-07T05:23:33Z | |
| dc.date.available | 2026-07-07T05:23:33Z | |
| dc.description | The k-th Fitting ideal of the Alexander invariant B of an arrangement A of n complex hyperplanes defines a characteristic subvariety, V_k(A), of the complex algebraic n-torus. In the combinatorially determined case where B decomposes as a direct sum of local Alexander invariants, we obtain a complete description of V_k(A). For any arrangement A, we show that the tangent cone at the identity of this variety coincides with R^1_k(A), one of the cohomology support loci of the Orlik-Solomon algebra. Using work of Arapura and Libgober, we conclude that all positive-dimensional components of V_k(A) are combinatorially determined, and that R^1_k(A) is the union of a subspace arrangement in C^n, thereby resolving a conjecture of Falk. We use these results to study the reflection arrangements associated to monomial groups. | |
| dc.description | LaTeX2e, 20 pages. A reference to Libgober's recent work in math.AG/9801070 is added. Several points are clarified, a new example is included | |
| dc.identifier | https://arxiv.org/abs/math/9801048 | |
| dc.identifier | http://arxiv.org/abs/math/9801048 | |
| dc.identifier | Mathematical Proceedings of the Cambridge Philosophical Society 127 (1999), no. 1, 33-53 | |
| dc.identifier | doi:10.1017/S0305004199003576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76483 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | Geometric Topology | |
| dc.subject | 14M12, 52B30 (Primary); 14H30, 20F36, 57M05 (Secondary) | |
| dc.title | Characteristic varieties of arrangements | |
| dc.type | text |