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...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| 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:2445/217940 |
| Acceso en línea: | https://hdl.handle.net/2445/217940 |
| Access Level: | acceso abierto |
| Palabra clave: | Corbes modulars Geometria algebraica Modular curves Algebraic geometry |
| Sumario: | 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. |
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