On real forms of Belyi surfaces with symmetric groups of automorphisms
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2012
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BIRKHAUSER VERLAG AG
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Etayo Gordejuela, J. J., Gromadzki, G. & Martínez García, E. «On Real Forms of Belyi Surfaces With Symmetric Groups of Automorphisms». Mediterranean Journal of Mathematics, vol. 9, n.o 4, noviembre de 2012, pp. 669-75. DOI.org (Crossref), https://doi.org/10.1007/s00009-011-0140-x.
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.