Monodromy groups of parameterized linear differential equations with regular singularities (Q2918785)

The authors consider systems of ordinary linear differential equations on Riemann's sphere and families of such systems depending analytically on complex parameters. (An important class of such families are the isomonodromic deformations of systems with regular singular points.) For such families they study the notion of regular singularities. They prove an analogue of the Schlesinger theorem for systems with regular singularities and solve both a parameterized version of the weak Riemann-Hilbert Problem and a special case of the inverse problem in parameterized Picard-Vessiot theory.