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| HAL : hal-00656992, version 1 |
| arXiv : 1201.1499 |
| Fiche détaillée |  Récupérer au format |
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| Construction et classification de certaines solutions algébriques des systèmes de Garnier |
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| Karamoko Diarra 1 |
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| (05/01/2012) |
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| 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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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Géométrie analytique |
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| Domaine | : | Mathématiques/Géométrie algébrique |
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| Équations différentielles ordinaires – Déformations isomonodromiques – Familles de Hurwitz |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00656992, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00656992 | |
| oai:hal.archives-ouvertes.fr:hal-00656992 | |
| Contributeur : Dominique Hervé | |
| Soumis le : Jeudi 5 Janvier 2012, 16:12:34 | |
| Dernière modification le : Jeudi 5 Janvier 2012, 16:50:11 | |
