Moduli spaces of connections and Higgs bundles and geometry of spectral curves (I)


Masa-Hiko Saito

10:30:00 - 12:00:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

This is a joint work with Szilard Szabo in Budapest. We consider the moduli spaces of parabolic connections and parabolic Higgs bundles on a smooth projective curve C with singularities. After reviewing the constructions of the moduli spaces as smooth quasi-projective schemes, we will introduce a way to define canonical coordinate systems on a Zariski open set of these moduli spaces. By using these canonical coordinates, we can investigate some interesting geometric structures of the moduli spaces, Lagrangian fibrations and some duality on the moduli spaces. Isomonodromic deformations of connections give nonlinear differential equations with "Painleve property". I will explain how these structures are related to the geometry of spectral curves.

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