Vector bundles and theta functions on curves of genus 2 and 3
| dc.creator | Beauville, Arnaud | |
| dc.date | 2004-06-02 | |
| dc.date.accessioned | 2026-07-07T05:08:48Z | |
| dc.date.available | 2026-07-07T05:08:48Z | |
| dc.description | Let C be a curve of genus g, and let SU(r) be the moduli space of vector bundles of rank r on C, with trivial determinant. A general E in SU(r) defines a theta divisor in the linear system |r Theta|, where Theta is the canonical theta divisor in Pic^{g-1}(C). This defines a rational map SU(r) - - > |r Theta|, which is the map associated to the determinant bundle on SU(r) (the positive generator of Pic(SU(r)). In this paper we prove that in genus 2 this map is generically finite and dominant. The same method, together with some classical work of Morin, shows that in rank 3 and genus 3 the theta map is a finite morphism -- in other words, every E in SU(3) admits a theta divisor. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406030 | |
| dc.identifier | http://arxiv.org/abs/math/0406030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71407 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H60 | |
| dc.title | Vector bundles and theta functions on curves of genus 2 and 3 | |
| dc.type | text |