| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Research Abstract |
M. Inaba and I constructed the moduli spaces of stable parabolic connections over a nonsingular projective curve with fixed formal type of regular or irregular singularities as non singular algebraic varieties. Moreover,we proved that the Riemann-Hilbert correspondence for these cases give an analytic isomorphism, which implies the geometric Painleve property for iso-monodromic or iso-Stokes non-linear differential equations. Together with Frank Loray, we constructed a good model of the moduli space of rank 2 stable parabolic connections over the projective line as well as its compactification. We found unexpected relations between two Lagrangian fibrations of the moduli space of connections and the classical duality of the projective space and its dual projective space. S. Szabo and I are developing a theory of apparent singularities of connections and Higgs bundles and try to understand the geometric Langlands correspondence.
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