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Abelian integrals in holomorphic foliations

Hossein Movasati
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Abstract

The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact 1-forms in this theory. As an application we identify some irreducible components of the space of holomorphic foliations of a fixed degree and with a center singularity in the projective space of dimension two. Also we calculate higher Melnikov functions under some generic conditions.

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Hossein Movasati. 2004-07-05. Abelian integrals in holomorphic foliations. https://arxiv.org/abs/math/0203062

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