Construction et classification de certaines solutions alg\'ebriques des syst\`emes de Garnier
Algebraic Geometry
2012-01-09 v1
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.
Cite
@article{arxiv.1201.1499,
title = {Construction et classification de certaines solutions alg\'ebriques des syst\`emes de Garnier},
author = {Karamoko Diarra},
journal= {arXiv preprint arXiv:1201.1499},
year = {2012}
}
Comments
22 pages