Fourier Transform and Prym varieties
Let $P$ be the Prym variety attached to an unramified double covering $\tilde{C} \rightarrow C$. Let $X=X(\tilde{\boldsymbol{C}}, C)$ be the variety of special divisors which birationally parametrizes the theta divisor in $P$. We prove that $X$ is the projectivization of the Fourier-Mukai transform...
| Autor: | |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2003 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/197442 |
| Acesso em linha: | https://hdl.handle.net/2445/197442 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Corbes algebraiques Geometria algebraica Algebraic curves Algebraic geometry |
| Resumo: | Let $P$ be the Prym variety attached to an unramified double covering $\tilde{C} \rightarrow C$. Let $X=X(\tilde{\boldsymbol{C}}, C)$ be the variety of special divisors which birationally parametrizes the theta divisor in $P$. We prove that $X$ is the projectivization of the Fourier-Mukai transform of a coherent sheaf $p_*(M)$, where $M$ is an invertible sheaf on $\tilde{C}$ and $p: \tilde{C} \rightarrow P$ is the natural embedding. We apply this fact to give an algebraic proof of the following Torelli type statement proved by Smith and Varley in the complex case: under some hypothesis the variety $X$ determines the covering $\tilde{C} \rightarrow C$. |
|---|