Calculation of mixed Hodge structures, Gauss-Manin connections and Picard-Fuchs equations

Details Calculation of mixed Hodge structures, Gauss-Manin connections and Picard-Fuchs equations Calculation of mixed Hodge structures, Gauss-Manin connections and Picard-Fuchs equations

2004-12-13

arxiv.org/abs/math/0412235v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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.

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