论文标题
曲线模量空间的某些覆盖物上的全态1形
Holomorphic 1-forms on some coverings of the moduli space of curves
论文作者
论文摘要
在本文中，我们考虑了Moduli空间$ \ MATHCAL {M} _g $ g $ $ g $的光滑射击复杂曲线的未经密码。在有限的扩展地图上的分支基因座上的一些假设下，我们证明，在$ \ Mathcal {m} _g $的平滑基因座的预先映射的前，霍明型1形式的矢量空间消失了。这适用于几个模量空间，作为带有2级结构的曲线的模量空间，自旋曲线和PRYM曲线的模量空间。特别是，我们得到的是，在Prym基因座的平滑开放式集合中没有非平凡的骨膜1形。
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 2-level structures, of spin curves and of Prym curves. In particular, we obtain that there are no non-trivial holomorphic 1-forms on the smooth open set of the Prym locus.
