Convolution of Picard–Fuchs Equations

Abstract

We determine explicit generators for a cohomology group constructed from a solution of a Fuchsian linear differential equation and describe its relation with cohomology groups with coefficients in a local system. In the parametrized case, this yields into an algorithm which computes new Fuchsian differential equations from those depending on multi-parameters. This generalizes the classical convolution of solutions of Fuchsian differential equations.