Belyi Functions Related to Plane Graphs: Multiplicities and Parasitic Solutions

Elena Kreines ()
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Elena Kreines: Moscow State University, Department of Higher Algebra, Faculty of Mathematics and Mechanics

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 468-475 from Springer

Abstract: Abstract In his classical work [3] A. Grothendieck put forward a theory of Dessins d’enfants which provides a plenty of new and non-trivial interrelations between different structures in category theory, algebra, algebraic geometry, complex analysis, topology, etc. The equivalence between categories of dessins d’enfants and Belyi pairs is among the key directions of this theory. In particular, this equivalence establishes an approach to a visualization of algebraic curves over number fields and to an interpretation of the action of Galois group Aut( $$ \bar Q$$ ) on the set of their isomorphism classes.

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_44

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