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

Abstract

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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Cited by in corpus (5)

• Conformal limits and the Bialynicki-Birula stratification of the space of lambda-connections
• Non-Abelian Hodge Theory and Related Topics
• Normal forms for rank two linear irregular differential equations and moduli spaces
• Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
• Moduli of Higgs bundles over the five punctured sphere