Revista Matemática Iberoamericana

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.

Article information

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

Dates
First available in Project Euclid: 2 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1080928425

Mathematical Reviews number (MathSciNet)
MR2076777

Zentralblatt MATH identifier
1055.37057

Subjects
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]

Keywords
holomorphic foliations holonomy Picard-Lefschetz theory

Citation

Movasati, Hossein. Abelian integrals in holomorphic foliations. Rev. Mat. Iberoamericana 20 (2004), no. 1, 183--204. https://projecteuclid.org/euclid.rmi/1080928425


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References

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