JournalsrmiVol. 23, No. 3pp. 793–810

On uniqueness of automorphisms groups of Riemann surfaces

  • Maximiliano Leyton A.

    Université Grenoble I, Saint-Martin-d'Hères, France
  • Rubén A. Hidalgo

    Universidad Técnica Federico Santa María, Valparaíso, Chile
On uniqueness of automorphisms groups of Riemann surfaces cover
Download PDF

Abstract

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

Cite this article

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

DOI 10.4171/RMI/513