Abelian integrals in holomorphic foliations.

Hossein Movasati

Revista Matemática Iberoamericana (2004)

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

Abstract

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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.

How to cite

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Movasati, 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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