Dessins d'enfants for analysts

Vincent Beffara

Preprints, Working Papers, ... Year :

Dessins d'enfants for analysts

(1)

Vincent Beffara

Function : Author
PersonId : 3387
IdHAL : vincent-beffara
ORCID : 0000-0002-6928-318X
IdRef : 080234577

Unité de Mathématiques Pures et Appliquées

Abstract

We present an algorithmic way of exactly computing Belyi functions for hypermaps and triangulations in genus $0$ or $1$, and the associated dessins, based on a numerical iterative approach initialized from a circle packing combined with subsequent lattice reduction. The main advantage compared to previous methods is that it is applicable to much larger graphs; we use very little algebraic geometry, and aim for this paper to be as self-contained as possible.

Keywords

Riemann surface Belyi function Dessin d'enfant

Domains

Mathematics [math] Complex Variables [math.CV] Mathematics [math] Algebraic Geometry [math.AG]

Fichier principal

Belyi_analysts.pdf (2.55 Mo)

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