Apparent singularities of Fuchsian equations and the Painlevé property for Garnier systems

We study movable singularities of Garnier systems using the connection of the latter with Schlesinger isomonodromic deformations of Fuchsian systems. Questions on the existence of solutions for some inverse monodromy problems are also considered.

► Movable singularities of the Garnier system are studied.
► We use the connection of the system with Schlesinger isomonodromic deformations.
► Some inverse monodromy problems for scalar equations are also considered.