Details
| Original language | English |
|---|---|
| Pages (from-to) | 2147-2165 |
| Number of pages | 19 |
| Journal | Pure and Applied Mathematics Quarterly |
| Volume | 20 |
| Issue number | 5 |
| Publication status | Published - 4 Nov 2024 |
Abstract
In this paper, we consider unramified coverings of the moduli space Mg 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 Mg. This applies to several moduli spaces, as the moduli space of curves with 2-level 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. a/iQDPrwdR9b6Ou2pH/ib1KPMMoRqQJXm.
Keywords
- coverings, holomorphic forms, Moduli space
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Pure and Applied Mathematics Quarterly, Vol. 20, No. 5, 04.11.2024, p. 2147-2165.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Holomorphic 1-forms on some coverings of the moduli space of curves
AU - Favale, Filippo Francesco
AU - Naranjo, Juan Carlos
AU - Pirola, Gian Pietro
AU - Torelli, Sara
N1 - Publisher Copyright: © 2024, International Press, Inc.. All rights reserved.
PY - 2024/11/4
Y1 - 2024/11/4
N2 - In this paper, we consider unramified coverings of the moduli space Mg 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 Mg. This applies to several moduli spaces, as the moduli space of curves with 2-level 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. a/iQDPrwdR9b6Ou2pH/ib1KPMMoRqQJXm.
AB - In this paper, we consider unramified coverings of the moduli space Mg 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 Mg. This applies to several moduli spaces, as the moduli space of curves with 2-level 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. a/iQDPrwdR9b6Ou2pH/ib1KPMMoRqQJXm.
KW - coverings
KW - holomorphic forms
KW - Moduli space
UR - http://www.scopus.com/inward/record.url?scp=85211317661&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2210.0712
DO - 10.48550/arXiv.2210.0712
M3 - Article
AN - SCOPUS:85211317661
VL - 20
SP - 2147
EP - 2165
JO - Pure and Applied Mathematics Quarterly
JF - Pure and Applied Mathematics Quarterly
SN - 1558-8599
IS - 5
ER -