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

被引：0

作者：

Favale, Filippo Francesco ^{[1
]}

Naranjo, Juan Carlos ^{[2
,3
]}

Pirola, Gian Pietro ^{[4
]}

Torelli, Sara ^{[5
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Roberto Cozzi 55, I-20125 Milan, Italy

[2] Univ Barcelona, Dept Matemat & Informat, Gran Via 585, Barcelona 08007, Spain

[3] Ctr Recerca Matemat, Edifici C,Campus Bellaterra, Bellaterra 08193, Spain

[4] Univ Pavia, Dipartimento Matemat, Via Ferrata 5, I-27100 Pavia, Italy

[5] Leibniz Univ Hannover, Inst Algebra Geometrie, Welfengarten 1, D-30167 Hannover, Germany

来源：

PURE AND APPLIED MATHEMATICS QUARTERLY | 2024年 / 20卷 / 05期

关键词：

Moduli space; holomorphic forms; coverings; MAPPING CLASS GROUP; SUBGROUPS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider unramified coverings of the moduli space 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 M-g. 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.

引用

页码：2147 / 2165

页数：19

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