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...

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Bibliographic Details
Authors: Marcucci, Valeria Ornella, Naranjo del Val, Juan Carlos
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
Description
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.