1. bookVolume 30 (2022): Edition 2 (May 2022)
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17 May 2013
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Characterization of second type plane foliations using Newton polygons

Publié en ligne: 02 Jun 2022
Volume & Edition: Volume 30 (2022) - Edition 2 (May 2022)
Pages: 103 - 123
Reçu: 06 Jul 2021
Accepté: 30 Sep 2021
Détails du magazine
License
Format
Magazine
eISSN
1844-0835
Première parution
17 May 2013
Périodicité
1 fois par an
Langues
Anglais
Abstract

In this article we characterize the foliations that have the same Newton polygon that their union of formal separatrices, they are the foliations called of the second type. In the case of cuspidal foliations studied by Loray [Lo], we precise this characterization using the Poincaré-Hopf index. This index also characterizes the cuspidal foliations having the same process of singularity reduction that the union of its separatrices. Finally we give necessary and sufficient conditions when these cuspidal foliations are generalized curves, and a characterization when they have only one separatrix.

Keywords

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