Revista Matemática Iberoamericana

On uniqueness of automorphisms groups of Riemann surfaces

Rubén A. Hidalgo and Maximiliano Leyton A.

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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.

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Rev. Mat. Iberoamericana, Volume 23, Number 3 (2007), 793-810.

First available in Project Euclid: 27 February 2008

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Primary: 30F10: Compact Riemann surfaces and uniformization [See also 14H15, 32G15] 30F35: Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx] 30F40: Kleinian groups [See also 20H10]

Riemann surfaces orbifolds Kleinian groups automorphisms


Leyton A. , Maximiliano; Hidalgo, Rubén A. On uniqueness of automorphisms groups of Riemann surfaces. Rev. Mat. Iberoamericana 23 (2007), no. 3, 793--810.

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