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March, 2004 Abelian integrals in holomorphic foliations
Hossein Movasati
Rev. Mat. Iberoamericana 20(1): 183-204 (March, 2004).


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. "Abelian integrals in holomorphic foliations." Rev. Mat. Iberoamericana 20 (1) 183 - 204, March, 2004.


Published: March, 2004
First available in Project Euclid: 2 April 2004

zbMATH: 1055.37057
MathSciNet: MR2076777

Primary: 14D99 , 32G34 , 57R30

Keywords: holomorphic foliations , holonomy , Picard-Lefschetz theory

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.20 • No. 1 • March, 2004
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