- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:44
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
20
2004
1
Abelian integrals in holomorphic foliations
Hossein
Movasati
IMPA, RIO DE JANEIRO, BRAZIL
Holomorphic foliations, holonomy, Picard-Lefschetz theory
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.
Manifolds and cell complexes
Algebraic geometry
Several complex variables and analytic spaces
General
183
204
10.4171/RMI/385
http://www.ems-ph.org/doi/10.4171/RMI/385