Dicritical singularities and laminar currents on Levi-flat hypersurfaces

TL;DR

This paper provides a practical criterion based on Segre varieties to identify dicritical singularities in Levi-flat hypersurfaces and offers a structural understanding of certain currents in the nondicritical case.

Contribution

It introduces an effective, Segre variety-based criterion for dicritical singularities and characterizes currents in nondicritical Levi-flat hypersurfaces.

Findings

Established a criterion for dicritical singularities using Segre varieties

Derived a structure theorem for currents in nondicritical cases

Enhanced understanding of Levi-flat hypersurface singularities

Abstract

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.