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Dessins d’enfants and genus zero actions Duong, Linh Ton

Abstract

A Dessin D'Enfant is a cellular map on a Riemann surface ramified over {0, 1, ∞}. We will describe Grothendieck's correspondence between the set of isomorphism classes of dessins and the set of ismorphism classes of algebraic curves defined over Q. We also describe the action of the Galois group of the algebraic numbers, Gal(Q/Q), on the dessins. Finally, we also talk about groups that admit genus zero actions on Riemann surfaces and investigate the nature of Belyi functions on these Riemann surfaces.

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