English

Character varieties, hexagonal 3-webs and Hess connection

Algebraic Geometry 2025-07-11 v1 Complex Variables Symplectic Geometry

Abstract

We investigate the existence of some affine structure on SL 2 (C)-character varieties on the four-punctured sphere through web and symplectic geometry. This work provides a new proof of non integrability (i.e. irreducibility) of Painlev{\'e} VI equations, previously proved by S. Cantat and the third author.

Keywords

Cite

@article{arxiv.2507.07542,
  title  = {Character varieties, hexagonal 3-webs and Hess connection},
  author = {Adjaratou Arame Diaw and Karamoko Diarra and Frank Loray and Tangue Ndawa Bertuel},
  journal= {arXiv preprint arXiv:2507.07542},
  year   = {2025}
}
R2 v1 2026-07-01T03:54:26.879Z