Foliations on the moduli space of rank two connections on the projective line minus four points - Laboratoire Jean-Alexandre Dieudonné Accéder directement au contenu
Chapitre D'ouvrage Année : 2013

Foliations on the moduli space of rank two connections on the projective line minus four points

Frank Loray
Masa-Hiko Saito
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Carlos Simpson

Résumé

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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Dates et versions

hal-00547446 , version 1 (16-12-2010)
hal-00547446 , version 2 (10-06-2011)

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Frank Loray, Masa-Hiko Saito, Carlos Simpson. Foliations on the moduli space of rank two connections on the projective line minus four points. D. Bertrand, Ph. Boalch, J.-M. Couveignes, P. Dèbes. Geometric and differential Galois theories, Société Mathématique de France, pp.115-168, 2013, Séminaires et Congrès n° 27. ⟨hal-00547446v2⟩
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