Families of simple Jacobians with many automorphisms

We study an explicit ( $2 g-1$ )-dimensional family of Jacobian varieties of dimension $\frac{1}{2}(d-1)(g-1)$, arising from quotient curves of unramified cyclic coverings of prime degree $d$ of hyperelliptic curves of genus $g \geqslant 2$. By using a deformation argument, we prove that the generic...

Descripción completa

Detalles Bibliográficos
Autores: Naranjo del Val, Juan Carlos, Ortega, Angela, Pirola, Gian Pietro, Spelta, Irene
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
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:2445/224822
Acceso en línea:https://hdl.handle.net/2445/224822
Access Level:acceso abierto
Palabra clave:Formes de Jacobi
Varietats abelianes
Jacobi forms
Abelian varieties
id ES_578be18fcdb2cf03ffb9c022c8c7b9be
oai_identifier_str oai:recercat.cat:2445/224822
network_acronym_str ES
network_name_str España
repository_id_str
spelling Families of simple Jacobians with many automorphismsNaranjo del Val, Juan CarlosOrtega, AngelaPirola, Gian PietroSpelta, IreneFormes de JacobiVarietats abelianesJacobi formsAbelian varietiesWe study an explicit ( $2 g-1$ )-dimensional family of Jacobian varieties of dimension $\frac{1}{2}(d-1)(g-1)$, arising from quotient curves of unramified cyclic coverings of prime degree $d$ of hyperelliptic curves of genus $g \geqslant 2$. By using a deformation argument, we prove that the generic element of the family is simple. Furthermore, we completely describe their endomorphism algebra, and we show that they admit a rank $\frac{1}{2}(d-1)-1$ group of non-polarized automorphisms. As an application of these results, we prove the generic injectivity of the Prym map for étale cyclic coverings of hyperelliptic curves of odd prime degree under some slight numerical restrictions. This result generalizes in several directions previous results on genus 2 .Foundation Compositio Mathematica2025202520252025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion19 p.application/pdfhttps://hdl.handle.net/2445/224822Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: https://doi.org/10.14231/AG-2025-026Algebraic Geometry, 2025, vol. 12, num.6, p. 869-887https://doi.org/10.14231/AG-2025-026cc-by-nc (c) Naranjo, J.C. et al., 2025http://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/2248222026-05-29T05:05:01Z
dc.title.none.fl_str_mv Families of simple Jacobians with many automorphisms
title Families of simple Jacobians with many automorphisms
spellingShingle Families of simple Jacobians with many automorphisms
Naranjo del Val, Juan Carlos
Formes de Jacobi
Varietats abelianes
Jacobi forms
Abelian varieties
title_short Families of simple Jacobians with many automorphisms
title_full Families of simple Jacobians with many automorphisms
title_fullStr Families of simple Jacobians with many automorphisms
title_full_unstemmed Families of simple Jacobians with many automorphisms
title_sort Families of simple Jacobians with many automorphisms
dc.creator.none.fl_str_mv Naranjo del Val, Juan Carlos
Ortega, Angela
Pirola, Gian Pietro
Spelta, Irene
author Naranjo del Val, Juan Carlos
author_facet Naranjo del Val, Juan Carlos
Ortega, Angela
Pirola, Gian Pietro
Spelta, Irene
author_role author
author2 Ortega, Angela
Pirola, Gian Pietro
Spelta, Irene
author2_role author
author
author
dc.subject.none.fl_str_mv Formes de Jacobi
Varietats abelianes
Jacobi forms
Abelian varieties
topic Formes de Jacobi
Varietats abelianes
Jacobi forms
Abelian varieties
description We study an explicit ( $2 g-1$ )-dimensional family of Jacobian varieties of dimension $\frac{1}{2}(d-1)(g-1)$, arising from quotient curves of unramified cyclic coverings of prime degree $d$ of hyperelliptic curves of genus $g \geqslant 2$. By using a deformation argument, we prove that the generic element of the family is simple. Furthermore, we completely describe their endomorphism algebra, and we show that they admit a rank $\frac{1}{2}(d-1)-1$ group of non-polarized automorphisms. As an application of these results, we prove the generic injectivity of the Prym map for étale cyclic coverings of hyperelliptic curves of odd prime degree under some slight numerical restrictions. This result generalizes in several directions previous results on genus 2 .
publishDate 2025
dc.date.none.fl_str_mv 2025
2025
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/224822
url https://hdl.handle.net/2445/224822
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.14231/AG-2025-026
Algebraic Geometry, 2025, vol. 12, num.6, p. 869-887
https://doi.org/10.14231/AG-2025-026
dc.rights.none.fl_str_mv cc-by-nc (c) Naranjo, J.C. et al., 2025
http://creativecommons.org/licenses/by-nc/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc (c) Naranjo, J.C. et al., 2025
http://creativecommons.org/licenses/by-nc/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 19 p.
application/pdf
dc.publisher.none.fl_str_mv Foundation Compositio Mathematica
publisher.none.fl_str_mv Foundation Compositio Mathematica
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869408459508678656
score 15,811543

Similares en LA Referencia