Six results on Painleve VI

Details Six results on Painleve VI Six results on Painleve VI

2005-03-02

arxiv.org/abs/math/0503043v3

Mathematics

Algebraic Geometry

16 pages, written for Angers 2004 International Conference on Asymptotic Theories and Painleve Equations (updated, added Remar

Scientific paper

After recalling some of the geometry of the sixth Painleve equation, we will describe how the Okamoto symmetries arise naturally from symmetries of Schlesinger's equations and summarise the classification of the Platonic Painleve six solutions. A key observation is that Painleve VI governs the isomonodromic deformations of certain Fuchsian systems on rank \emph{three} bundles.

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