On the Geometry of Isomonodromic Deformations

Details On the Geometry of Isomonodromic Deformations On the Geometry of Isomonodromic Deformations

2008-04-01

arxiv.org/abs/0804.0249v1

Physics

Mathematical Physics

20 pages

Scientific paper

10.1016/j.geomphys.2008.05.013

This note examines the geometry behind the Hamiltonian structure of isomonodromy deformations of connections on vector bundles over Riemann surfaces. The main point is that one should think of an open set of the moduli of pairs $(V,\nabla)$ of vector bundles and connections as being obtained by "twists" supported over points of a fixed vector bundle $V_0$ with a fixed connection $\nabla_0$; this gives two deformations, one, isomonodromic, of $(V,\nabla)$, and another induced from the isomonodromic deformation of $(V_0,\nabla_0)$. The difference between the two will be Hamiltonian.

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