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 $\hat{I}{›}^2/dH\wedge \hat{I}{›}^1$ 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.

A separate section discusses Fuchsian properties of the Picard-Fuchs system, Morse condition exterminated. Few errors were corrected