Local polar invariants for plane singular foliations

2015/08/27 by Cano, Felipe, Corral, Nuria, Mol, Rogério · 2 citations
#14C21 #32S65 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.06882

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 Poincaré problem with polar invariants.

Cited by

• On the k-th Milnor and k-th Tjurina Numbers of a Foliation
• On some indices of foliations and applications

Related

• The Poincaré problem in the dicritical case
• Invariant theory of foliations of the projective plane
• Sliding invariants and classification of singular holomorphic foliations in the plane
• Residue-type indices and holomorphic foliations
• Global dynamics and perspectives on singularities of holomorphic foliations