Local polar invariants for plane singular foliations
Felipe Cano, Nuria Corral, Rog\'erio Mol
TL;DR
This survey explores how polar invariants can be used to analyze plane singular foliations, providing characterizations, descriptions, and interpretations related to their local and global properties.
Contribution
It offers a comprehensive overview of polar invariants' role in understanding non-dicritical holomorphic foliations and their invariant curves, including new characterizations and interpretations.
Findings
Characterization of second type foliations
Description of GSV-index via polar curves
Interpretation of Poincaré problem proofs
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\'e problem with polar invariants.
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