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Author Lebl, Jiri
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-05-12
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Complex Variables ♦ Mathematics - Algebraic Geometry ♦ 32S25 ♦ 32S65 ♦ 32C07 ♦ 14P15 ♦ math
Abstract 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.
Description Reference: J. Geom. Anal., 22 (2012), no. 2, 410-432
Educational Use Research
Learning Resource Type Article
Page Count 21


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