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 Riemannsurfaces for genera $g \ge {3(p-1)\over 2}$,that are multiple of ${p-1 \over2}$. This is a generalization of the results obtained in \cite{[BCI1]} forpentagonal Riemann surfaces, and the results of \cite{[K]} and \cite{[CI3]} forzero- and one-dimensional isolated strata in the branch locus.
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机译：$ g $的紧致黎曼曲面的模空间$ \ mathcal {M} _ {g} $具有双折结构，并且这种双折点的奇异点集是\ textit {分支轨迹} $ \ mathcal {B} _ {g} $。给定质数$ p \ ge 7 $，$ \ mathcal {B} _ {g} $包含由$ p $ -ge黎曼曲面组成的孤立层，属类$ g \ ge {3（p-1）\ over 2} $，是$ {p-1 \ over2} $的倍数。这是对\ cite {[BCI1]}五角形Riemann曲面中的结果以及\ cite {[K]}和\ cite {[CI3]}的零分支和一维孤立层中的结果的概括。轨迹。
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