Algebraic separatrices for non-dicritical foliations on projective spaces of dimension at least four

  • Jorge Vitório Pereira
Original Paper


Non-dicritical codimension one foliations on projective spaces of dimension four or higher always have an invariant algebraic hypersurface. The proof relies on a strengthening of a result by Rossi on the algebraization/continuation of analytic subvarieties of projective spaces.


Foliations Algebraic separatrices Extension of subvarieties 

Mathematics Subject Classification

37F75 32D15 



J. V. Pereira thanks Dominique Cerveau and Stefan Kebekus for their remarks about this work and acknowledges the support of CNPq, Faperj, and Freiburg Institute for Advanced Studies (FRIAS). The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Programme (FP7/2007-2013) under REA Grant agreement no. 609305.


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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.IMPARio de JaneiroBrazil
  2. 2.FRIASFreiburgGermany

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