Levi-Flat Hypersurfaces Tangent to Projective Foliations

Let M⊂ℙn be a singular real-analytic Levi-flat hypersurface tangent to a codimension-one holomorphic foliation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{F}$\end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{F}$\end{document} can be defined by a global closed meromorphic 1-form.