Global Prym-Torelli for double coverings ramified in at least 6 points
We prove that the ramified Prym map $\mathcal{P}_{g, r}$ which sends a covering $\pi: D \longrightarrow C$ ramified in $r$ points to the Prym variety $P(\pi):=\operatorname{Ker}\left(N m_\pi\right)$ is an embedding for all $r \geq 6$ and for all $g(C)>0$. Moreover, by studying the restriction to...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | 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:2445/191946 |
| Acceso en línea: | https://hdl.handle.net/2445/191946 |
| Access Level: | acceso abierto |
| Palabra clave: | Corbes algebraiques Geometria algebraica Algebraic curves Algebraic geometry |
| Sumario: | We prove that the ramified Prym map $\mathcal{P}_{g, r}$ which sends a covering $\pi: D \longrightarrow C$ ramified in $r$ points to the Prym variety $P(\pi):=\operatorname{Ker}\left(N m_\pi\right)$ is an embedding for all $r \geq 6$ and for all $g(C)>0$. Moreover, by studying the restriction to the locus of coverings of hyperelliptic curves, we show that $\mathcal{P}_{g, 2}$ and $\mathcal{P}_{g, 4}$ have positive dimensional fibers. |
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