Finite subschemes of abelian varieties and the Schottky problem
The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians, among indecomposable principally polarized abelian varieties $(A,\Theta)$ of dimension $g$, by the existence of $g+2$ points $\Gamma \subset A$ in special position with respect to $2 \Theta$, but general with respect to $\The...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/124869 |
| Acesso em linha: | https://hdl.handle.net/2445/124869 |
| Access Level: | acceso abierto |
| Palavra-chave: | Corbes Varietats abelianes Curves Abelian varieties |
| Resumo: | The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians, among indecomposable principally polarized abelian varieties $(A,\Theta)$ of dimension $g$, by the existence of $g+2$ points $\Gamma \subset A$ in special position with respect to $2 \Theta$, but general with respect to $\Theta$, and furthermore states that such collections of points must be contained in an Abel-Jacobi curve. Building on the ideas in the original paper, we give here a self contained, scheme theoretic proof of the theorem, extending it to finite, possibly nonreduced subschemes $\Gamma$. |
|---|