Rigidity and prolongability of differential equations and the study of global structure

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We constructed a framework for the global study of linear ordinary differential equations and holonomic systems in several variables by using the notion of rigidity and spectral types and the operation called middle convolution. We succeeded to define the middle convolution for holonomic systems, which brings a new structure on the moduli space of holonomic systems. In some cases, middle convolution connects an ordinary differential equation to a holonomic system, and then we can compare various structures among ODEs and holonomic systems.