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| HAL : hal-00547446, version 2 |
| arXiv : 1012.3612 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (16-12-2010) | v2 (10-06-2011) |
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| Foliations on the moduli space of rank two connections on the projective line minus four points |
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| Frank Loray 1Masa-Hiko Saito 2 |
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| (16/12/2010) |
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| We look at natural foliations on the Painlevé VI moduli space of regular connections of rank $2$ on $\pp ^1 -\{ t_1,t_2,t_3,t_4\}$. These foliations are fibrations, and are interpreted in terms of the nonabelian Hodge filtration, giving a proof of the nonabelian Hodge foliation conjecture in this case. Two basic kinds of fibrations arise: from apparent singularities, and from quasiparabolic bundles. We show that these are transverse. Okamoto's additional symmetry, which may be seen as Katz's middle convolution, exchanges the quasiparabolic and apparent-singularity foliations. |
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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 – INSA Rennes – Université Rennes II |
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| 2 : | Department of Mathematics |
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Kobe University |
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| 3 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS) |
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| Géométrie analytique |
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| Domaine | : | Mathématiques/Géométrie algébrique |
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| hal-00547446, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00547446 | |
| oai:hal.archives-ouvertes.fr:hal-00547446 | |
| Contributeur : Carlos Simpson | |
| Soumis le : Vendredi 10 Juin 2011, 10:11:31 | |
| Dernière modification le : Vendredi 10 Juin 2011, 16:13:31 | |
