Dicritical singularities and laminar currents on Levi-flat hypersurfaces
  We establish an effective criterion for a dicritical singularity of a real analytic Levi-flat hypersurface. The criterion is stated in terms of the Segre varieties. As an application, we obtain a structure theorem for some class of currents in the nondicritical case. 
Sergey Pinchuk, Rasul Shafikov, and Alexandre Sukhov
math.CV math.DS