Finite braid group orbits in Aff(C)-character varieties of the punctured sphere

2016/04/14 by Gaël Cousin, Delphine Moussard, Cousin, Gaël +1
Mathematics · Physics and Astronomy · #14F35 #20F36 #20F55 #33C70 #34M56 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1604.04234

openalex publication_date 2016/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a complete description of finite braid group orbits in Aff(C)-character varieties of the punctured Riemann sphere. This is performed thanks to a coalescence procedure and to the theory of finite complex reflection groups. We then derive consequences in the theory of differential equations. These concern algebraicity of isomonodromic deformations for reducible rank two logarithmic connections on the sphere, the Riemann-Hilbert problem and F_D-type Lauricella hypergeometric functions.

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