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The symplectic and twistor geometry of the general isomonodromic deformation problem

N. M. J. Woodhouse
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Abstract

Hitchin's twistor treatment of Schlesinger's equations is extended to the general isomonodromic deformation problem. It is shown that a generic linear system of ordinary differential equations with gauge group SL(n,C) on a Riemann surface X can be obtained by embedding X in a twistor space Z on which sl(n,C) acts. When a certain obstruction vanishes, the isomonodromic deformations are given by deforming X in Z. This is related to a description of the deformations in terms of Hamiltonian flows on a symplectic manifold constructed from affine orbits in the dual Lie algebra of a loop group.

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N. M. J. Woodhouse. 2000-07-18. The symplectic and twistor geometry of the general isomonodromic deformation problem. https://doi.org/10.1016/s0393-0440(01)00003-1

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