### Impacto

Etayo Gordejuela, J. Javier and Gromadzki, G. and Martínez García, Ernesto
*On real forms of Belyi surfaces with symmetric groups of automorphisms.*
Mediterranean journal of mathematics, 9
.
ISSN 1660-5446

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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.

Item Type: | Article |
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Uncontrolled Keywords: | Automorphisms of Riemann surfaces – symmetries – Singerman symmetries – ovals – Fuchsian groups – Belyi surfaces – real forms |

Subjects: | Sciences > Mathematics > Group Theory |

ID Code: | 15818 |

References: | Belyi G.: On Galois extensions of a maximal cyclotomic field. Math. USSR Izv. 14, 247–256 (1980) H.S.M. Coxeter, W.O. J. Moser, Generators and Relations for Discrete Groups. 4th ed. Springer–Verlag (Berlin), 1980, ix+169 pp. Gromadzki G.: On Singerman symmetries of a class of Belyi Riemann surfaces. J. Pure Appl. Algebra 213, 1905–1910 (2009) Harnack A.: Über die Vieltheiligkeit der ebenen algebraischen Kurven. Math. Ann. 10, 189–199 (1876) Köck B., Singerman D.: Real Belyi Theory. Q. J. Math. 58, 463–478 (2007) Köck B., Lau E.: A note on Belyi’s theorem for Klein surfaces. Q. J. Math. 61, 103–107 (2010) W. Ledermann, Introduction to Group Theory. Oliver and Boyd (Edinburgh), 1973, vii+176 pp. Singerman D.: Symmetries of Riemann surfaces with large automorphism group. Math. Ann. 210, 17–32 (1974) J. Wolfart, The “obvious” part of Belyi’s theorem and Riemann surfaces with many automorphisms. Geometric Galois actions, 1, 97–112, London Math. Soc. Lecture Note Ser., 242, 1997. |

Deposited On: | 03 Jul 2012 10:32 |

Last Modified: | 06 Feb 2014 10:32 |

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