Journal of Geometric Analysis

, Volume 22, Issue 2, pp 410–432 | Cite as

Algebraic Levi-Flat Hypervarieties in Complex Projective Space

  • Jiří Lebl


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 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.


Singular Levi-flat hypersurface Segre variety Holomorphic foliation of projective space 

Mathematics Subject Classification (2000)

32S25 32S65 32C07 14P15 


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© Mathematica Josephina, Inc. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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