Arkiv för Matematik

Volume 56 (2018)

Number 2

On dicritical singularities of Levi-flat sets

Pages: 395 – 408



Sergey Pinchuk (Department of Mathematics, Indiana University, Bloomington, Indiana, U.S.A.)

Rasul Shafikov (Department of Mathematics, University of Western Ontario, London, Ontario, Canada)

Alexandre Sukhov (U.F.R. de Mathématiques, Université de Lille (Sciences et Technologies), Villeneuve d’Ascq, France)


It is proved that dicritical singularities of real analytic Levi-flat sets coincide with the set of Segre degenerate points.


Levi-flat set, dicritical singularity, foliation, Segre variety

2010 Mathematics Subject Classification

32Dxx, 32Sxx, 34Mxx, 37F75

The second author is partially supported by the Natural Sciences and Engineering Research Council of Canada. The third author is partially supported by Labex CEMPI.

Received 21 August 2017

Accepted 29 December 2017

Published 24 May 2022