2002/03/31 by Hossein Movasati
Mathematics · #math.AG #msc:57R30 #msc:14D99 #msc:32G34
published as Rev. Mat. Iberoamericana 20 (2004),183-204 · 24 pages
arxiv created 2004/07/05 · arxiv updated 2009/11/30
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.