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On the Chekhov-Fock coordinates of dessins d'enfants

G. Shabat·V. Zolotarskaia
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Abstract

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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G. Shabat, V. Zolotarskaia. 2002-10-12. On the Chekhov-Fock coordinates of dessins d'enfants. https://arxiv.org/abs/math/0210183

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