An Introduction to Belyi Surfaces
نویسنده
چکیده
We outline the basic theory of Belyi surfaces, up to Belyi’s theorem (1979, [1]), which characterizes these spaces as precisely those Riemann surfaces that are defined over Q. We then detail the Brooks-Makover construction of a Belyi surface from an oriented cubic graph from [3]. Consequently, we can apply the model of Bollobás in order to randomly pick a Belyi surface. Finally, we briefly explain the relationship between Belyi surfaces and Grothendieck’s dessins d’enfants.
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