English

Differential relations for almost Belyi maps

Algebraic Geometry 2018-09-07 v2

Abstract

Several kinds of differential relations for polynomial components of almost Belyi maps are presented. Saito's theory of free divisors give particularly interesting (yet conjectural) logarithmic action of vector fields. The differential relations implied by Kitaev's construction of algebraic Painleve VI solutions through pull-back transformations are used to compute almost Belyi maps for the pull-backs giving all genus 0 and 1 Painleve VI solutions in the Lisovyy-Tykhyy classification.

Cite

@article{arxiv.1701.03302,
  title  = {Differential relations for almost Belyi maps},
  author = {Raimundas Vidunas and Jiro Sekiguchi},
  journal= {arXiv preprint arXiv:1701.03302},
  year   = {2018}
}

Comments

Typos corrected; 21 pages; 1 table

R2 v1 2026-06-22T17:48:28.767Z