Publications Mathématiques de Besançon
Algèbre et Théorie des Nombres
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J. Sijsling; J. Voight
On computing Belyi maps
Publications mathématiques de Besançon no. 1 (2014), p. 73-131, doi: 10.5802/pmb.5
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Class. Math.: 11G32, 11Y40
Mots clés: Belyi maps, dessins d’enfants, covers, uniformization, computational algebra

Résumé

Nous donnons un aperçu des méthodes actuelles pour le calcul des revêtements de la droite projective ramifiés en au plus trois points, connus sous le nom de morphismes de Belyĭ. Ces méthodes comprennent une approche directe, se ramenant à la solution d’un système d’équations polynomiales ainsi que des méthodes analytiques complexes, de formes modulaires et $p$-adiques. Ce faisant, nous posons quelques questions et donnons de nombreux exemples.

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