Monodromy groups of parameterized linear differential equations with regular singularities

Abstract

We study the notion of regular singularities for parameterized complex ordinary linear differential systems, 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.

Version to appear in the Bulletin of the London Mathematical Society

Cited by in corpus (11)

• Parameterized Picard-Vessiot extensions and Atiyah extensions
• Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations
• Isomonodromic differential equations and differential categories
• Unipotent differential algebraic groups as parameterized differential Galois groups
• A density theorem for parameterized differential Galois theory
• Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence
• Difference algebraic relations among solutions of linear differential equations
• Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation
• Parameterized Differential Equations over k((t))(x)
• Calculating Galois groups of third order linear differential equations with parameters
• Some applications of the parameterized Picard-Vessiot theory