Revista Matemática Iberoamericana

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Volume 20, Issue 1, 2004, pp. 183–204
DOI: 10.4171/RMI/385

Published online: 2004-04-30

Abelian integrals in holomorphic foliations

Hossein Movasati[1]

(1) IMPA, Rio de Janeiro, Brazil

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.

Keywords: Holomorphic foliations, holonomy, Picard-Lefschetz theory

Movasati Hossein: Abelian integrals in holomorphic foliations. Rev. Mat. Iberoam. 20 (2004), 183-204. doi: 10.4171/RMI/385