ar X iv : 0 80 5 . 17 63 v 2 [ m at h . C V ] 1 4 Ju l 2 00 9 SINGULAR LEVI - FLAT HYPERSURFACES IN COMPLEX PROJECTIVE SPACE
نویسنده
چکیده
We study singular real-analytic Levi-flat hypersurfaces in complex projective space. We give necessary and sufficient conditions for such a hypersurface to be a pullback of a real-analytic curve in C via a meromorphic function. We define the rank of a real hypersurface and study the connections between rank, degree, and the type and size of the singularity for Levi-flat hypersurfaces. Finally, we study degenerate singularities of algebraic Levi-flat hypersurfaces. Among other examples, we construct a nonalgebraic semianalytic Levi-flat hypersurface with compact leaves that is a perturbation of an algebraic Levi-flat variety.
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