Belyi map verification using certified path tracking
Number Theory
2026-04-20 v1 Algebraic Geometry
Abstract
We provide an end-to-end workflow to rigorously compute the monodromy of Belyi maps from exact equations over number fields using certified homotopy continuation. We then apply this method at scale to certify the monodromy triples of Belyi maps in the -functions and Modular Forms Database (LMFDB).
Cite
@article{arxiv.2604.15562,
title = {Belyi map verification using certified path tracking},
author = {Alexandre Guillemot and John Voight},
journal= {arXiv preprint arXiv:2604.15562},
year = {2026}
}