Modules of Abelian integrals and Picard-Fuchs systems

Details Modules of Abelian integrals and Picard-Fuchs systems Modules of Abelian integrals and Picard-Fuchs systems

2001-10-11

arxiv.org/abs/math/0110126v3

Mathematics

Dynamical Systems

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

Scientific paper

We give a simple proof of an isomorphism between the two
$\mathbb{C}[t]$-modules: the module of relative cohomologies $\Lambda^2/dH\land
\Lambda^1$ 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.

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