On the Geometry of Isomonodromic Deformations

Abstract

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.

20 pages

References in corpus (3)

• Dual Isomonodromic Deformations and Moment Maps to Loop Algebras
• Symplectic Manifolds and Isomonodromic Deformations
• The symplectic and twistor geometry of the general isomonodromic deformation problem

Cited by in corpus (8)

• Hamiltonian structure of rational isomonodromic deformation systems
• Flat rank 2 vector bundles on genus 2 curves
• An Interpretation of Some Hitchin Hamiltonians In Terms of Isomonodromic Deformation
• Description of generalized isomonodromic deformations of rank two linear differential equations using apparent singularities
• Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections
• Hecke Modifications, Wonderful Compactifications and Moduli of Principal Bundles
• The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations
• Unfolding of the unramified irregular singular generalized isomonodromic deformation