On Real Forms of Belyi Surfaces With Symmetric Groups of Automorphisms
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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
KeywordsAutomorphisms of Riemann surfaces symmetries Singerman symmetries ovals Fuchsian groups Belyi surfaces real forms
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