Levi-Flat Hypersurfaces Tangent to Projective Foliations

Abstract

Let M⊂ℙn be a singular real-analytic Levi-flat hypersurface tangent to a codimension-one holomorphic foliation \(\mathcal{F}\) on ℙn. For n≥3, we give sufficient conditions to guarantee the existence of degenerate singularities in M, (in the sense of Segre varieties) and as a consequence we prove that \(\mathcal{F}\) can be defined by a global closed meromorphic 1-form.