Separation properties of theta functions
| dc.creator | Esteves, Eduardo | |
| dc.date | 1997-09-08 | |
| dc.date.accessioned | 2026-07-07T09:07:24Z | |
| dc.date.available | 2026-07-07T09:07:24Z | |
| dc.description | In a 1993 article, G. Faltings gave a new construction of the moduli space $U$ of semistable vector bundles on a smooth curve $X$, avoiding geometric invariant theory. Roughly speaking, Faltings showed that the normalisation $B$ of the ring $A$ of theta functions (associated with vector bundles on $X$) suffices to realize $U$ as a projective variety. Describing Faltings' work, C.S. Seshadri asked how close $A$ is to $B$. In this article, we address this question from a geometric point of view. We consider the rational map, $π: U @>>> Proj(A)$, and show that, not only is $π$ defined everywhere, but also $π$ is bijective, and is an isomorphism over the stable locus of $U$, if the characteristic of the ground field is 0. Moreover, we give a direct local construction of $U$ as a fine moduli space, when the rank and degree are coprime, in any characteristic. The methods in the article apply to singular curves as well. | |
| dc.description | AMS-TeX, 27 pages - address: esteves@impa.br | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9709008 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9709008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150361 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Separation properties of theta functions | |
| dc.type | text |