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

2010/12/16 by Loray, Frank, Saito, Masa-Hiko, Simpson, Carlos T.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1012.3612

Abstract

We look at natural foliations on the Painlevé VI moduli space of regular connections of rank 2 on \pp ¹ -t₁,t₂,t₃,t₄. 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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