Revista Matemática Iberoamericana

Abelian integrals in holomorphic foliations

Hossein Movasati

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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.

Article information

Rev. Mat. Iberoamericana, Volume 20, Number 1 (2004), 183-204.

First available in Project Euclid: 2 April 2004

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Zentralblatt MATH identifier

Primary: 57R30: Foliations; geometric theory 14D99: None of the above, but in this section 32G34: Moduli and deformations for ordinary differential equations (e.g. Knizhnik-Zamolodchikov equation) [See also 34Mxx]

holomorphic foliations holonomy Picard-Lefschetz theory


Movasati, Hossein. Abelian integrals in holomorphic foliations. Rev. Mat. Iberoamericana 20 (2004), no. 1, 183--204.

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