Belyi maps from zeroes of hypergeometric polynomials
Algebraic Geometry
2025-03-26 v2 Classical Analysis and ODEs
Abstract
Evaluation of low degree hypergeometric polynomials to zero defines an algebraic hypersurface in the affine space of the free parameters and the argument. This article investigates the algebraic surfaces 2F1(-N,b;c;z)=0 for N=3 and N=4. As a captivating application, these surfaces parametrize certain families of genus 0 Belyi maps.
Keywords
Cite
@article{arxiv.2402.16826,
title = {Belyi maps from zeroes of hypergeometric polynomials},
author = {Raimundas Vidunas},
journal= {arXiv preprint arXiv:2402.16826},
year = {2025}
}
Comments
Added Remark 6.8, extra references, corrections; 29 pages; 3 figures