Local polar invariants for plane singular foliations

In this survey paper, we take the viewpoint of polar invariants to the local and global study of non-dicritical holomorphic foliation 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...

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Bibliographic Details
Published in:Expositiones mathematicae 2019-06, Vol.37 (2), p.145-164
Main Authors: Cano, Felipe, Corral, Nuria, Mol, Rogério
Format: Article
Language:English
Subjects:
Holomorphic foliation
Invariant curves
Polar curves
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Summary:In this survey paper, we take the viewpoint of polar invariants to the local and global study of non-dicritical holomorphic foliation 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.
ISSN:0723-0869
1878-0792
DOI:10.1016/j.exmath.2018.01.003