On dicritical singularities of Levi-flat sets
Sergey Pinchuk, Rasul Shafikov, Alexandre Sukhov
TL;DR
This paper establishes that dicritical singularities of real analytic Levi-flat sets are exactly the points where Segre degeneracy occurs, linking geometric singularities with algebraic degeneracy conditions.
Contribution
It proves the equivalence between dicritical singularities and Segre degenerate points in Levi-flat sets, clarifying their geometric and algebraic relationship.
Findings
Dicritical singularities coincide with Segre degenerate points.
Provides a characterization of singularities in Levi-flat sets.
Bridges geometric and algebraic perspectives on Levi-flat sets.
Abstract
It is proved that dicritical singularities of real analytic Levi-flat sets coincide with the set of Segre degenerate points.
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