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.
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}
}