Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/217940
Title: Holomorphic 1-forms on some coverings of the Moduli space of curves
Author: Favale, Filippo Francesco
Naranjo del Val, Juan Carlos
Pirola, Gian Pietro
Torelli, Sara
Keywords: Corbes modulars
Geometria algebraica
Modular curves
Algebraic geometry
Issue Date: 4-Nov-2024
Abstract: 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.
Note: Reproducció del document publicat a: https://doi.org/10.4310/PAMQ.241105054319
It is part of: 2024, vol. 20, num.5, p. 2147-2165
URI: https://hdl.handle.net/2445/217940
Related resource: https://doi.org/10.4310/PAMQ.241105054319
ISSN: 1558-8599
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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