Prym varieties of double coverings of elliptic curves
We prove the generic injectivity of the Prym map $\mathscr{P}: \mathcal{R}_{1, r} \rightarrow \mathcal{A}_{\frac{r}{2}}^\delta$ sending a double covering of an elliptic curve ramified at $r \geq 6$ points to its polarized Prym variety. For $r=6$ the map is birational and both $\mathcal{R}_{1,6}$ and...
| Authors: | , |
|---|---|
| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/197423 |
| Online Access: | https://hdl.handle.net/2445/197423 |
| Access Level: | Open access |
| Keyword: | Corbes algebraiques Geometria algebraica Algebraic curves Algebraic geometry |
| Summary: | We prove the generic injectivity of the Prym map $\mathscr{P}: \mathcal{R}_{1, r} \rightarrow \mathcal{A}_{\frac{r}{2}}^\delta$ sending a double covering of an elliptic curve ramified at $r \geq 6$ points to its polarized Prym variety. For $r=6$ the map is birational and both $\mathcal{R}_{1,6}$ and $\mathcal{A}_3^\delta$ are unirational. |
|---|