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arXiv · 2507.07542

Character varieties, hexagonal 3-webs and Hess connection

Adjaratou Arame Diaw·Karamoko Diarra·Frank Loray·Tangue Ndawa Bertuel
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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.

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Adjaratou Arame Diaw, Karamoko Diarra, Frank Loray, Tangue Ndawa Bertuel. 2025-07-10. Character varieties, hexagonal 3-webs and Hess connection. https://arxiv.org/abs/2507.07542

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