本文讨论了n-marked黎曼球面模空间上自然的对称群作用,计算出其全部的不动点及n-marked黎曼球面的对称类型,同时讨论了黎曼球面上SL(2,C)作用的动力系统特征,得出其周期性的一个描述,并在这些基础上给出n-punctured黎曼球面模空间的奇性刻画．

In this paper,we discuss the natural action of symmetric group on the moduli space of n-marked Riemannian spheres.We calculated out all the fixed points of this action and all the symmetric types of n-marked Riemannian sphere.We also discussed the dynamic property of the action of SL(2,C) on Riemannian sphere,so as to give a description of the periodic property of this action.Basing on this,we give a description of the singularity of the moduli space of n-punctured Riemannian sphere.