Finite orbits of the pure braid group on the monodromy of the\n 2-variable Garnier system

2017/05/09 by Pierpaolo Calligaris, Calligaris, Pierpaolo, Marta Mazzocco +1
Mathematics · Physics and Astronomy · #32G34 #33E17 #34M55 #34M56 #53D30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1705.03295

openalex publication_date 2017/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that the SL₂( mathbb C) character variety of the\nRiemann sphere \Σ₅ with five boundary components is a 5-parameter\nfamily of affine varieties of dimension 4. We endow this family of affine\nvarieties with an action of the braid group and classify exceptional finite\norbits. This action represents the nonlinear monodromy of the 2 variable\nGarnier system and finite orbits correspond to algebraic solutions.\n

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