Abelian integrals in holomorphic foliations
Movasati, Hossein
Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, p. 183-204 / Harvested from Project Euclid
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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.
Publié le : 2004-03-14
Classification:  holomorphic foliations,  holonomy,  Picard-Lefschetz theory,  57R30,  14D99,  32G34 
@article{1080928425,
     author = {Movasati, Hossein},
     title = {Abelian integrals in holomorphic foliations},
     journal = {Rev. Mat. Iberoamericana},
     volume = {20},
     number = {1},
     year = {2004},
     pages = { 183-204},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1080928425}
}

Movasati, Hossein. Abelian integrals in holomorphic foliations. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp.  183-204. http://gdmltest.u-ga.fr/item/1080928425/