Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations

TL;DR

This paper investigates the conditions under which dicritical singularities occur in holomorphic foliations tangent to Levi-flat hypersurfaces, providing new insights into their structure and applications in complex geometry.

Contribution

It establishes hypotheses ensuring the existence of dicritical singularities and applies these results to foliations in the complex projective plane.

Findings

Conditions guaranteeing dicritical singularities

Existence results for foliations in compact complex surfaces

Applications to Levi-flat hypersurfaces in projective space

Abstract

We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these objects. As consequence, we give some applications to holomorphic foliations tangent to real-analytic Levi-flat hypersurfaces with singularities in $\mathbb{P}^2$.