On the Chekhov-Fock coordinates of dessins d'enfants

Details On the Chekhov-Fock coordinates of dessins d'enfants On the Chekhov-Fock coordinates of dessins d'enfants

2002-10-12

arxiv.org/abs/math/0210183v1

Mathematics

Algebraic Geometry

9 pages

Scientific paper

There are several ways to associate a complex structure to a ribbon graph. In the construction of dessins d'enfants a single riemann surface is associated to each graph. We call it the Grothendieck model of a ribbon graph. The goal of the present paper is to discuss one more such construction, depending on some parameters - that of Chekhov-Fock. We prove that putting all parametres equal to 0, we obtain the Grothendieck model of this graph.

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