Algebraic Levi-flat hypervarieties in complex projective space

Details Algebraic Levi-flat hypervarieties in complex projective space Algebraic Levi-flat hypervarieties in complex projective space

2008-05-13

arxiv.org/abs/0805.1763v4

J. Geom. Anal., 22 (2012), no. 2, 410-432

Mathematics

Complex Variables

21 pages, latex amsart, amsrefs; A couple of very minor typos fixed, added journal reference

Scientific paper

10.1007/s12220-010-9201-9

We study singular real-analytic Levi-flat hypersurfaces in complex projective space. We define the rank of an algebraic Levi-flat hypersurface and study the connections between rank, degree, and the type and size of the singularity. In particular, we study degenerate singularities of algebraic Levi-flat hypersurfaces. We then give necessary and sufficient conditions for a Levi-flat hypersurface to be a pullback of a real-analytic curve in $\mathbb{C}$ via a meromorphic function. 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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