English

On computing Belyi maps

Number Theory 2018-11-13 v3 Algebraic Geometry Complex Variables Group Theory

Abstract

We survey methods to compute three-point branched covers of the projective line, also known as Belyi maps. These methods include a direct approach, involving the solution of a system of polynomial equations, as well as complex analytic methods, modular forms methods, and p-adic methods. Along the way, we pose several questions and provide numerous examples.

Keywords

Cite

@article{arxiv.1311.2529,
  title  = {On computing Belyi maps},
  author = {Jeroen Sijsling and John Voight},
  journal= {arXiv preprint arXiv:1311.2529},
  year   = {2018}
}

Comments

57 pages, 3 figures, extensive bibliography; English and French abstract; revised according to referee's suggestions

R2 v1 2026-06-22T02:05:10.605Z