Algebraic isomonodromic deformations of the five punctured sphere arising from quintic plane curves

2016/12/04 by Arnaud Girand, Girand, Arnaud
Mathematics · #14E22 #20G05 #20G20 #32D15 #32G08 #32G34 #34M50 #34M56 #51N15 #55R10 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1612.01168

openalex publication_date 2016/12/04 · openalex created_date 2016/12/16 · openalex updated_date 2026/07/28

Abstract

In this paper, we classify the algebraic isomonodromic deformations that can be obtained through restriction to generic lines of logarithmic flat connections on the complex projective plane ℙ²_ℂ whose singular locus is a quintic curve. We then explicitly compute the (finite) finite mapping class group orbits of the associated points in the character variety and describe the new algebraic Garnier solutions that can be obtained through this procedure.

Related

• Algebraic isomonodromic deformations of logarithmic connections on the Riemann sphere and finite braid group orbits on character varieties
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• Ramified covers and tame isomonodromic solutions on curves
• Isomonodromic deformations in genus zero and one: algebrogeometric solutions and Schlesinger transformations