Abelian integrals in holomorphic foliations

• Autores: Hossein Movasati
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 20, Nº 1, 2004, págs. 183-204
• Idioma: inglés
• DOI: 10.4171/rmi/385
• Títulos paralelos:
  • Integrales abelianas en foliaciones holomorfas
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• Resumen

  • 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.