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...

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Detalles Bibliográficos
Autores: Naranjo del Val, Juan Carlos, Ortega, Angela
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu: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
Descripción
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.