arXiv math/01101262001-10math.DSmath.CV

Modules of Abelian integrals and Picard-Fuchs systems

D. Novikov

备注：: A separate section discusses Fuchsian properties of the Picard-Fuchs system, Morse condition exterminated. Few errors were corrected
DOI：: 10.1088/0951-7715/15/5/305

英文摘要：

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.

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