# Abelian integrals in holomorphic foliations.

Revista Matemática Iberoamericana (2004)

- Volume: 20, Issue: 1, page 183-204
- ISSN: 0213-2230

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topMovasati, Hossein. "Abelian integrals in holomorphic foliations.." Revista Matemática Iberoamericana 20.1 (2004): 183-204. <http://eudml.org/doc/39630>.

@article{Movasati2004,

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.},

author = {Movasati, Hossein},

journal = {Revista Matemática Iberoamericana},

keywords = {Integrales abelianas; Foliaciones; Variedades complejas; Variedades diferenciables; limit cycles; Hilbert's 16th problem; algebro-geometric approach; Picard-Lefschetz theory},

language = {eng},

number = {1},

pages = {183-204},

title = {Abelian integrals in holomorphic foliations.},

url = {http://eudml.org/doc/39630},

volume = {20},

year = {2004},

}

TY - JOUR

AU - Movasati, Hossein

TI - Abelian integrals in holomorphic foliations.

JO - Revista Matemática Iberoamericana

PY - 2004

VL - 20

IS - 1

SP - 183

EP - 204

AB - 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.

LA - eng

KW - Integrales abelianas; Foliaciones; Variedades complejas; Variedades diferenciables; limit cycles; Hilbert's 16th problem; algebro-geometric approach; Picard-Lefschetz theory

UR - http://eudml.org/doc/39630

ER -

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