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On Real Forms of Belyi Surfaces With Symmetric Groups of Automorphisms

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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.

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Authors and Affiliations

  1. Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense, 28040, Madrid, Spain

    José Javier Etayo

  2. Instytut Matematyki, Uniwersytet Gdański, Wita Stwosza 57, 80–952, Gdańsk, Poland

    Grzegorz Gromadzki

  3. Departamento de Matemáticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040, Madrid, Spain

    Ernesto Martínez

Authors
  1. José Javier Etayo
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  2. Grzegorz Gromadzki
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  3. Ernesto Martínez
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Corresponding author

Correspondence to Ernesto Martínez.

Additional information

The first author is partially supported by UCM910444 and MTM2008–00272, the second one by the Research Grant NN 201 366436 of the Polish Ministry of Science and Higher Education and the third one by MTM2008–00250.

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Etayo, J.J., Gromadzki, G. & Martínez, E. On Real Forms of Belyi Surfaces With Symmetric Groups of Automorphisms. Mediterr. J. Math. 9, 669–675 (2012). https://doi.org/10.1007/s00009-011-0140-x

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  • DOI: https://doi.org/10.1007/s00009-011-0140-x

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