Computing Euclidean Belyi maps

TL;DR

This paper presents an explicit algorithm for computing Euclidean Belyi maps, which are special three-point branched covers of the complex projective line, expanding computational tools in algebraic geometry.

Contribution

The paper introduces a new algorithm specifically designed for Euclidean Belyi maps, filling a gap in computational methods for these geometric objects.

Findings

Algorithm successfully computes Euclidean Belyi maps

Provides explicit examples of such maps

Enhances computational techniques in algebraic geometry

Abstract

We exhibit an explicit algorithm to compute three-point branched covers of the complex projective line when the uniformizing triangle group is Euclidean.