Very ampleness for Theta on the compactified Jacobian
| dc.creator | Esteves, Eduardo | |
| dc.date | 1997-09-05 | |
| dc.date.accessioned | 2026-07-07T09:07:24Z | |
| dc.date.available | 2026-07-07T09:07:24Z | |
| dc.description | The Jacobian $J$ of a complete, smooth, connected curve $X$ admits a canonical divisor $Θ$, called the Theta divisor. It is well-known that $Θ$ is ample and, in fact, $3Θ$ is very ample. For a general complete, integral curve $X$, D'Souza constructed a compactification $\bar J$ of the Jacobian $J$ by considering torsion-free, rank 1 sheaves on $X$. Soucaris and the author considered independently the analogous Theta divisor $Θ$ on $\bar J$, and showed that $Θ$ is ample. In this article, we show that $nΘ$ is very ample for $n$ greater or equal to a specified lower bound. If $X$ has at most ordinary nodes or cusps as singularities, then our lower bound is 3. Our main tool is to use theta sections associated to vector bundles on $X$ to embed $\bar J$ into a projective space. | |
| dc.description | AMS-TeX, 11 pages - address: esteves@impa.br | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9709005 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9709005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150359 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Very ampleness for Theta on the compactified Jacobian | |
| dc.type | text |