Isomonodromic Deformations on Riemann Surfaces

Some representations of a pair "a bundle with a connection" on a Riemann surface, based on a representation of a surface as a factor of an exterior of a unit disk, is introduced. In this representation isomonodromic deformations of bundles with logarithmic connections are described by some modification of the Schlesinger system on a Riemann sphere (typically this modification is just the ordinary Schlesinger system) plus some linear system.