English

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

R2 v1 2026-06-28T15:00:44.761Z