Abelian integrals in holomorphic foliations

Details Abelian integrals in holomorphic foliations Abelian integrals in holomorphic foliations

2002-03-07

arxiv.org/abs/math/0203062v3

Rev. Mat. Iberoamericana 20 (2004),183-204

Mathematics

Algebraic Geometry

24 pages

Scientific paper

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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