Coherent systems and Brill-Noether theory
| dc.creator | Bradlow, Steven | |
| dc.creator | Garcia-Prada, Oscar | |
| dc.creator | Muñoz, Vicente | |
| dc.creator | Newstead, Peter | |
| dc.date | 2002-05-30 | |
| dc.date.accessioned | 2026-07-07T04:48:48Z | |
| dc.date.available | 2026-07-07T04:48:48Z | |
| dc.description | Let $C$ be a curve of genus $g\geq 2$. A coherent system on $C$ consists of a pair $(E,V)$ where $E$ is an algebraic vector bundle of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of sections of $E$. The stability of the coherent systems depend on a parameter $τ$. We study the variation of the moduli space of coherent systems when we move the parameter. As an application, we analyse the cases $k=1,2,3$ and $n=2$ explicitly. For small values of $τ$, the moduli space of coherent systems is related to the Brill-Noether loci, the subspaces of the moduli space of stable bundles consisting of those bundles with a prescribed number of sections. The study of coherent systems is applied to find the dimension, irreducibility, and in some cases, the Picard group, of the Brill-Noether loci with $k\leq 3$. | |
| dc.description | 44 pages, Latex2e | |
| dc.identifier | https://arxiv.org/abs/math/0205317 | |
| dc.identifier | http://arxiv.org/abs/math/0205317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64188 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D20; 14H51; 14H60 | |
| dc.title | Coherent systems and Brill-Noether theory | |
| dc.type | text |