%0 Journal Article
%T Equivalence of Group Actions on Riemann Surfaces
%A Mariela Carvacho Bustamante
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1012.4337v1