Riemann Surfaces上群作用的等价性
Equivalence of Group Actions on Riemann Surfaces
摘要：
我们生产的每个自然数$n \geq 3$两个1-参数家庭的黎曼曲面承认自同构群与两个循环子群$H_{1}$和$H_{2}$的orden $2^{n}$，这是共轭的组中的定向保持同胚的相应的黎曼曲面，但不共轭组的共形自同构。这个性质意味着模空间$\mathcal{M}_{g}$的子簇$\mathcal{M}_{g}(H_{1})$不是正规子簇，该模空间由表示亏格$g$的黎曼曲面的点组成，该亏格允许一组拓扑共轭于$H_{1} $的自同构（等价于$H_{2}$）。
英文摘要：
We produce for each natural number $n \geq 3$ two 1--parameter families of Riemann surfaces admitting automorphism groups with two cyclic subgroups $H_{1}$ and $H_{2}$ of orden $2^{n}$, that are conjugate in the group of orientation--preserving homeomorphism of the corresponding Riemann surfaces, but not conjugate in the group of conformal automorphisms. This property implies that the subvariety $\mathcal{M}_{g}(H_{1})$ of the moduli space $\mathcal{M}_{g}$ consisting of the points representing the Riemann surfaces of genus $g$ admitting a group of automorphisms topologically conjugate to $H_{1} $ (equivalently to $H_{2}$) is not a normal subvariety.
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