A Family of Foliations with One Singularity

  • S. C. CoutinhoEmail author
  • Filipe Ramos Ferreira


For every integer \(k \ge 3\) we describe a new family of foliations of degree k with one singularity. We show that a very generic member of this family has trivial isotropy group and a line as its unique Darboux polynomial.


Holomorphic foliation Algebraic solution Singularity 

Mathematics Subject Classification

Primary 17B35 16S32 Secondary 37F75 



During the preparation of the paper the first author was partially supported by CNPq Grant 304543/2017-9 and the second author by a Grant PIBIC(CNPq). We also benefited from the access to on-line journals provided by CAPES. We would also like to thank the referee for numerous suggestions that greatly improved this paper.


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Copyright information

© Sociedade Brasileira de Matemática 2019

Authors and Affiliations

  1. 1.Departamento de Ciência da Computação, Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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