标题： 在模空间分支点中的p-角黎曼曲面的孤立层 显示英文标题

标题： On isolated strata of p-gonal Riemann surfaces in the branch locus of moduli spaces

摘要： 紧致黎曼曲面的模空间$\mathcal{M}_{g}$的亏格为$g$，具有轨道空间结构，这种轨道空间的奇异点集是\textit{分支点集} $\mathcal{B}_{g}$ 。 给定一个素数$p \ge 7$，$\mathcal{B}_{g}$包含由$p$边形黎曼曲面组成的孤立层，这些曲面的亏格为$g \ge {3(p-1)\over 2}$，且是${p-1 \over 2}$的倍数。 这是对在\cite{[BCI1]}中获得的五边形黎曼曲面结果的推广，以及对分支点集中的零维和一维孤立层的结果\cite{[K]}和\cite{[CI3]}的推广。 显示英文摘要

摘要： The moduli space $\mathcal{M}_{g}$ of compact Riemann surfaces of genus $g$ has orbifold structure, and the set of singular points of such orbifold is the \textit{branch locus} $\mathcal{B}_{g}$. Given a prime number $p \ge 7$, $\mathcal{B}_{g}$ contains isolated strata consisting of $p$-gonal Riemann surfaces for genera $g \ge {3(p-1)\over 2}$,that are multiple of ${p-1 \over 2}$. This is a generalization of the results obtained in \cite{[BCI1]} for pentagonal Riemann surfaces, and the results of \cite{[K]} and \cite{[CI3]} for zero- and one-dimensional isolated strata in the branch locus.