%0 Journal Article
%T Calculation of mixed Hodge structures, Gauss-Manin connections and Picard-Fuchs equations
%A Hossein Movasati
%J Mathematics
%D 2004
%I arXiv
%X In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimension $n$ in terms of differential forms. In the case $n=1$ such computations have many applications in differential equations and counting their limit cycles. For $n>3$, these computations give us an explicit definition of Hodge cycles.
%U http://arxiv.org/abs/math/0412235v1