Singular Levi-flat hypersurfaces and codimension one foliations

Marco Brunella

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)

  • Volume: 6, Issue: 4, page 661-672
  • ISSN: 0391-173X

Abstract

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We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.

How to cite

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Brunella, Marco. "Singular Levi-flat hypersurfaces and codimension one foliations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.4 (2007): 661-672. <http://eudml.org/doc/272273>.

@article{Brunella2007,
abstract = {We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.},
author = {Brunella, Marco},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {complex manifold; (singular) Levi-flat hypersurface; holomorphic foliation; resolution of singularities},
language = {eng},
number = {4},
pages = {661-672},
publisher = {Scuola Normale Superiore, Pisa},
title = {Singular Levi-flat hypersurfaces and codimension one foliations},
url = {http://eudml.org/doc/272273},
volume = {6},
year = {2007},
}

TY - JOUR
AU - Brunella, Marco
TI - Singular Levi-flat hypersurfaces and codimension one foliations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2007
PB - Scuola Normale Superiore, Pisa
VL - 6
IS - 4
SP - 661
EP - 672
AB - We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.
LA - eng
KW - complex manifold; (singular) Levi-flat hypersurface; holomorphic foliation; resolution of singularities
UR - http://eudml.org/doc/272273
ER -

References

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  1. [1] M. S. Baouendi, P. Ebenfelt and L. P. Rothschild, “Real Submanifolds in Complex Space and their Mappings”, Princeton Mathematical Series 47, 1999. Zbl0944.32040MR1668103
  2. [2] D. Burns and X. Gong, Singular Levi-flat real analytic hypersurfaces, Amer. J. Math.121 (1999), 23–53. Zbl0931.32009MR1704996
  3. [3] F. Cano, Reduction of the singularities of codimension one singular foliations in dimension three, Ann. of Math.160 (2004), 907–1011. Zbl1088.32019MR2144971
  4. [4] H. Cartan, Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France85 (1957), 77–99. Zbl0083.30502MR94830
  5. [5] D. Cerveau, Feuilletages holomorphes de codimension 1. Réduction des singularités en petites dimensions et applications, Panor. Synthèses 8 (1999), 11–47. Zbl1029.32015MR1760842
  6. [6] K. Diederich and J. E. Fornaess, Pseudoconvex domains with real-analytic boundary, Ann. of Math.107 (1978), 371–384. Zbl0378.32014MR477153
  7. [7] S. Lojasiewicz, “Introduction to Complex Analytic Geometry”, Birkhäuser, 1991. Zbl0747.32001MR1131081

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