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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Global Prym-Torelli for double coverings ramified in at least six points

Authors: Juan Carlos Naranjo and Angela Ortega
Journal: J. Algebraic Geom. 31 (2022), 387-396
Published electronically: December 28, 2021
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Abstract | References | Additional Information

Abstract: 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 $P(\pi )≔Ker(Nm_{\pi })$ is an embedding for all $r\ge 6$ 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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Additional Information

Juan Carlos Naranjo
Affiliation: Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Spain
MR Author ID: 318430
ORCID: 0000-0003-1989-4924

Angela Ortega
Affiliation: Institut für Mathematik, Humboldt Universität zu Berlin, Germany
MR Author ID: 726216

Received by editor(s): June 26, 2020
Received by editor(s) in revised form: November 4, 2020
Published electronically: December 28, 2021
Additional Notes: The first author was partially supported by the Proyecto de Investigación MTM2015-65361-PID2019-104047GB-100.
Article copyright: © Copyright 2021 University Press, Inc.