Modules of Abelian integrals and Picard-Fuchs systems

Abstract

We give a simple proof of an isomorphism between the two $\mathbb{C}[t]$-modules: the module of relative cohomologies $Λ^2/dH\land Λ^1$ and the module of Abelian integrals corresponding to a regular at infinity polynomial $H$ in two variables. Using this isomorphism, we prove existence and deduce some properties of the corresponding Picard-Fuchs system.