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Mediterranean Journal of Mathematics

, Volume 9, Issue 4, pp 669–675 | Cite as

On Real Forms of Belyi Surfaces With Symmetric Groups of Automorphisms

  • José Javier Etayo
  • Grzegorz Gromadzki
  • Ernesto MartínezEmail author
Article
  • 86 Downloads

Abstract

In virtue of the Belyi Theorem an algebraic curve can be defined over the algebraic numbers if and only if the corresponding Riemann surface can be uniformized by a subgroup of a Fuchsian triangle group. Such surfaces are known as Belyi surfaces. Here we study the actions of the symmetric groups S n on Belyi Riemann surfaces. We show that such surfaces are symmetric and we calculate the number of connected components of the corresponding real forms.

Mathematics Subject Classification (2010)

Primary 30F Secondary 14H 

Keywords

Automorphisms of Riemann surfaces symmetries Singerman symmetries ovals Fuchsian groups Belyi surfaces real forms 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • José Javier Etayo
    • 1
  • Grzegorz Gromadzki
    • 2
  • Ernesto Martínez
    • 3
    Email author
  1. 1.Departamento de Álgebra, Facultad de MatemáticasUniversidad ComplutenseMadridSpain
  2. 2.Instytut MatematykiUniwersytet GdańskiGdańskPoland
  3. 3.Departamento de Matemáticas FundamentalesUNEDMadridSpain

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