Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations

We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these objects. As consequence, we give some applications to holomorphic f...

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Bibliographic Details
Published in:Geometriae dedicata 2018-10, Vol.196 (1), p.35-44
Main Authors: Beltrán, Andrés, Fernández-Pérez, Arturo, Neciosup, Hernán
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Hyperspaces
Mathematical analysis
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Singularity (mathematics)
Topology
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Summary:We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these objects. As consequence, we give some applications to holomorphic foliations tangent to real-analytic Levi-flat hypersurfaces with singularities in P 2 .
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-017-0303-4