Characterization of second type plane foliations using Newton polygons

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, we precise this characterization using the Poincaré-Hopf index. This index...

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Bibliographic Details
Published in:arXiv.org 2018-12
Main Authors: Fernández-Sanchez, Percy, García Barroso, Evelia R, Saravia-Molina, Nancy
Format: Article
Language:English
Subjects:
Polygons
Online Access:Get full text
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Summary: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, we precise this characterization using the Poincaré-Hopf index. This index also characterizes the cuspidal foliations having the same desingularization 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1812.06530