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

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 ${\mathbb{P}}^2$.

arXiv comment11 pages, to appear in Geometriae Dedicata

References in corpus (5)

• Singular set of a Levi-flat hypersurface is Levi-flat
• Algebraic Levi-flat hypervarieties in complex projective space
• On Normal Forms of Singular Levi-Flat Real Analytic Hypersurfaces
• Existence of non-algebraic singularities of differential equation
• Dicritical singularities and laminar currents on Levi-flat hypersurfaces

Cited by in corpus (1)

• On real-analytic Levi-flat hypersurfaces and holomorphic webs