Galois Covers of Moduli of Curves
Galois Covers of Moduli of Curves
复制标题
曲线模的伽罗瓦覆盖
DOI：
10.1023/a:1001731524036
复制
发表时间：
2000
影响因子：
1.8
通讯作者：
Martin Pikaart
中科院分区：
文献类型：
--
作者：
M. Boggi;Martin Pikaart
研究了具有某种水平结构的尖曲线的模空间。我们证明了所谓的几何层次结构，在边界上遇到的水平是光滑的，如果周围的品种是光滑的，在某些情况下，我们可以明确地描述它们。光滑性意味着尖曲线的模空间（在任何域上）允许一个光滑的有限伽罗瓦覆盖。最后，我们证明了其中一些模空间是单连通的。
Moduli spaces of pointed curves with some level structure are studied. We prove that for so-called geometric level structures, the levels encountered in the boundary are smooth if the ambient variety is smooth, and in some cases we can describe them explicitly. The smoothness implies that the moduli space of pointed curves (over any field) admits a smooth finite Galois cover. Finally, we prove that some of these moduli spaces are simply connected.