Revista Matemática Iberoamericana

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Volume 23, Issue 3, 2007, pp. 793–810
DOI: 10.4171/RMI/513

Published online: 2007-12-31

On uniqueness of automorphisms groups of Riemann surfaces

Maximiliano Leyton A.[1] and Rubén A. Hidalgo[2]

(1) Université Grenoble I, Saint-Martin-d'Hères, France
(2) Universidad Técnica Federico Santa María, Valparaíso, Chile

Let $\gamma, r, s$, $ \geq 1$ be non-negative integers. If $p$ is a prime sufficiently large relative to the values $\gamma$, $r$ and $s$, then a group $H$ of conformal automorphisms of a closed Riemann surface $S$ of order $p^{s}$ so that $S/H$ has signature $(\gamma,r)$ is the unique such subgroup in $\mathrm{Aut}(S)$. Explicit sharp lower bounds for $p$ in the case $(\gamma,r,s) \in \{(1,2,1),(0,4,1)\}$ are provided. Some consequences are also derived.

Keywords: Riemann surfaces, orbifolds, Kleinian groups, automorphisms

Leyton A. Maximiliano, Hidalgo Rubén: On uniqueness of automorphisms groups of Riemann surfaces. Rev. Mat. Iberoam. 23 (2007), 793-810. doi: 10.4171/RMI/513