JournalsrmiVol. 20, No. 1pp. 183–204

Abelian integrals in holomorphic foliations

  • Hossein Movasati

    IMPA, Rio de Janeiro, Brazil
Abelian integrals in holomorphic foliations cover
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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.

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Hossein Movasati, Abelian integrals in holomorphic foliations. Rev. Mat. Iberoam. 20 (2004), no. 1, pp. 183–204

DOI 10.4171/RMI/385