Holomorphic 1-forms on some coverings of the Moduli space of curves

In this paper, we consider unramified coverings of the moduli space $\mathcal{M}_g$ of smooth projective complex curves of genus $g$. Under some hypothesis on the branch locus of the finite extended map to the Deligne-Mumford compactification, we prove the vanishing of the vector space of holomorphi...

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Authors: Favale, Filippo Francesco, Naranjo del Val, Juan Carlos, Pirola, Gian Pietro, Torelli, Sara
Format: article
Status:Published version
Publication Date:2024
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/217940
Online Access:https://hdl.handle.net/2445/217940
Access Level:Open access
Keyword:Corbes modulars
Geometria algebraica
Modular curves
Algebraic geometry
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spelling Holomorphic 1-forms on some coverings of the Moduli space of curvesFavale, Filippo FrancescoNaranjo del Val, Juan CarlosPirola, Gian PietroTorelli, SaraCorbes modularsGeometria algebraicaModular curvesAlgebraic geometryIn this paper, we consider unramified coverings of the moduli space $\mathcal{M}_g$ of smooth projective complex curves of genus $g$. Under some hypothesis on the branch locus of the finite extended map to the Deligne-Mumford compactification, we prove the vanishing of the vector space of holomorphic 1 -forms on the preimage of the smooth locus of $\mathcal{M}_g$. This applies to several moduli spaces, as the moduli space of curves with 2level structures, of spin curves and of Prym curves. In particular, we obtain that there are no nontrivial holomorphic 1 -forms on the smooth open set of the Prym locus.2025202520242025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion18 p.application/pdfhttps://hdl.handle.net/2445/217940Articles 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/10.4310/PAMQ.2411050543192024, vol. 20, num.5, p. 2147-2165https://doi.org/10.4310/PAMQ.241105054319cc-by (c) Favale, F. et al., 2024http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/2179402026-05-29T05:05:01Z
dc.title.none.fl_str_mv Holomorphic 1-forms on some coverings of the Moduli space of curves
title Holomorphic 1-forms on some coverings of the Moduli space of curves
spellingShingle Holomorphic 1-forms on some coverings of the Moduli space of curves
Favale, Filippo Francesco
Corbes modulars
Geometria algebraica
Modular curves
Algebraic geometry
title_short Holomorphic 1-forms on some coverings of the Moduli space of curves
title_full Holomorphic 1-forms on some coverings of the Moduli space of curves
title_fullStr Holomorphic 1-forms on some coverings of the Moduli space of curves
title_full_unstemmed Holomorphic 1-forms on some coverings of the Moduli space of curves
title_sort Holomorphic 1-forms on some coverings of the Moduli space of curves
dc.creator.none.fl_str_mv Favale, Filippo Francesco
Naranjo del Val, Juan Carlos
Pirola, Gian Pietro
Torelli, Sara
author Favale, Filippo Francesco
author_facet Favale, Filippo Francesco
Naranjo del Val, Juan Carlos
Pirola, Gian Pietro
Torelli, Sara
author_role author
author2 Naranjo del Val, Juan Carlos
Pirola, Gian Pietro
Torelli, Sara
author2_role author
author
author
dc.subject.none.fl_str_mv Corbes modulars
Geometria algebraica
Modular curves
Algebraic geometry
topic Corbes modulars
Geometria algebraica
Modular curves
Algebraic geometry
description In this paper, we consider unramified coverings of the moduli space $\mathcal{M}_g$ of smooth projective complex curves of genus $g$. Under some hypothesis on the branch locus of the finite extended map to the Deligne-Mumford compactification, we prove the vanishing of the vector space of holomorphic 1 -forms on the preimage of the smooth locus of $\mathcal{M}_g$. This applies to several moduli spaces, as the moduli space of curves with 2level structures, of spin curves and of Prym curves. In particular, we obtain that there are no nontrivial holomorphic 1 -forms on the smooth open set of the Prym locus.
publishDate 2024
dc.date.none.fl_str_mv 2024
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/2445/217940
url https://hdl.handle.net/2445/217940
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/10.4310/PAMQ.241105054319
2024, vol. 20, num.5, p. 2147-2165
https://doi.org/10.4310/PAMQ.241105054319
dc.rights.none.fl_str_mv cc-by (c) Favale, F. et al., 2024
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by (c) Favale, F. et al., 2024
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 18 p.
application/pdf
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
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score 15,81155

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