On the splitting type of the holomorphic vector bundles induced from Fuchsian system

Author: Gia Giorgadze
Co-authors: Gega Gulagashvili
Keywords: Splitting type, Fuchsian system
Annotation:

In the report we prove, that for any Fuchsian system of differential equa- tions on Riemann sphere there exists a rational matrix function whose partial indices coincide with the splitting type of holomorphic vector bundles in- duced from Fuchsian system. From this we obtain solution of the Riemann- Hilbert boundary value problem for piecewise constant matrix-function in closed form.

Lecture files:

On the splitting type of the vector bundles induces from Fuchsian system [en]