Semistable bundles on Riemann surfaces and isomonodromic deformations

We consider the Riemann-Hilbert problem and isomonodromic deformations of Fuchsian systems on a compact Riemann surface of genus g. On the Riemann surfaces of a positive genus the logarithmic connections in a semi-stable bundle of degree zero play the role of a Fuchsian system. This approach to the Riemann-Hilbert problem was first considered by H. Esnault and E. Viehweg. The equations for isomonodromic deformations of logarithmic connection on an elliptic curve will be derived using this approach. Also, we present the constructive local formula for the divisor of isomonodromic deformation and the new bound of slopes of Harder-Narasimhan stratification factors which is used in the local formula of divisor.