descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2019Embargo end date: 01 Jan 2015 English Publisher:Elsevier BVJournal:Expositiones Mathematicae, volume 37, pages 145-164 (issn: 0723-0869,

Authors: Cano, Felipe; Corral Pérez, Nuria; Mol, Rogério;

doi: 10.1016/j.exmath.2018.01.003 , 10.48550/arxiv.1508.06882

arXiv: 1508.06882

handle: 10902/34948

Local polar invariants for plane singular foliations

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Abstract

In this survey paper, we take the viewpoint of polar invariants to the local and global study of non-dicritical holomorphic foliations in dimension two and their invariant curves. It appears a characterization of second type foliations and generalized curve foliations as well as a description of the GSV-index in terms of polar curves. We also interpret the proofs concerning the Poincar�� problem with polar invariants.

Related Organizations

Universidade Federal de Minas Gerais
Brazil
UNIVERSIDADE DE SAO PAULO
Brazil
University of Cantabria
Spain
University of Valladolid
Spain

Keywords

Polar curves, holomorphic foliations, Dynamical Systems (math.DS), Invariant curves, polar curves, invariant curves, Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions, Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, Singularities of holomorphic vector fields and foliations, 32S65, 14C21, FOS: Mathematics, Dynamical aspects of holomorphic foliations and vector fields, Mathematics - Dynamical Systems, Holomorphic foliation

1 Research products, page 1 of 1

Local polar invariants and the Poincaré problem in the dicritical case
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