The fibers of the ramified Prym map

We study the ramified Prym map $\mathscr{P}_{g, r} \rightarrow \mathscr{A}_{g-1+\frac{r}{2}}^\delta$ which assigns to a ramified double cover of a smooth irreducible curve of genus $g$ ramified in $r$ points the Prym variety of the covering. We focus on the six cases where the dimension of the sourc...

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Detalles Bibliográficos
Autores: Frediani, Paola, Naranjo del Val, Juan Carlos, Spelta, Irene
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/191907
Acceso en línea:https://hdl.handle.net/2445/191907
Access Level:acceso abierto
Palabra clave:Corbes algebraiques
Geometria algebraica
Algebraic curves
Algebraic geometry
Descripción
Sumario:We study the ramified Prym map $\mathscr{P}_{g, r} \rightarrow \mathscr{A}_{g-1+\frac{r}{2}}^\delta$ which assigns to a ramified double cover of a smooth irreducible curve of genus $g$ ramified in $r$ points the Prym variety of the covering. We focus on the six cases where the dimension of the source is strictly greater than the dimension of the target giving a geometric description of the generic fiber. We also give an explicit example of a totally geodesic curve which is an irreducible component of a fiber of the Prym map $\mathscr{P}_{1,2}$.