Algorithms and differential relations for Belyi functions

Abstract

A tool package for computing genus 0 Belyi functions is presented, including simplification routines, computation of moduli fields, decompositions, dessins d'enfant. The main algorithm for computing the Belyi functions themselves is based on implied transformations of the hypergeometric differential equation to Fuchsian equations, preferably with few singular points. This gives interesting differential relations between polynomial components of a Belyi function.

29 pages, 1 fugure

References in corpus (1)

• Belyi functions for hyperbolic hypergeometric-to-Heun transformations

Cited by in corpus (6)

• Belyi functions for hyperbolic hypergeometric-to-Heun transformations
• Gauge Theories and Dessins d'Enfants: Beyond the Torus
• Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants
• Composite Genus One Belyi Maps
• Genus One Belyi Maps by Quadratic Correspondences
• Differential relations for almost Belyi maps