Middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangements

Abstract

The middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangements is defined as a natural generalization of the middle convolution for Fuchsian ordinary differential equations. Additivity of the generalized middle convolution is proved. It is observed that the singular locus may increase by the generalized middle convolution. Examples concerning with hypergeometric series in several variables are given.