Construction et classification de certaines solutions algébriques des systèmes de Garnier

2012/01/05 by Karamoko Diarra, Diarra, Karamoko
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.1201.1499

openalex publication_date 2012/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we classify all (complete) non elementary algebraic solutions of Garnier systems that can be constructed by Kitaev's method: they are deduced from isomonodromic deformations defined by pulling back a given fuchsian equation E by a family of ramified covers. We first introduce orbifold structures associated to a fuchsian equation. This allow to get a refined version of Riemann-Hurwitz formula and then to promtly deduce that E is hypergeometric. Then, we can bound exponents and degree of the pull-back maps and further list all possible ramification cases. This generalizes a result due to C. Doran for the Painleve VI case. We explicitely construct one of these solutions.

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