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Abelian integrals in holomorphic foliations

Algebraic Geometry 2007-05-23 v3

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.

Keywords

Cite

@article{arxiv.math/0203062,
  title  = {Abelian integrals in holomorphic foliations},
  author = {Hossein Movasati},
  journal= {arXiv preprint arXiv:math/0203062},
  year   = {2007}
}

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24 pages