Singular set of a Levi-flat hypersurface is Levi-flat
arXiv:1012.5993 · doi:10.1007/s00208-012-0821-1
Abstract
We study the singular set of a singular Levi-flat real-analytic hypersurface. We prove that the singular set of such a hypersurface is Levi-flat in the appropriate sense. We also show that if the singular set is small enough, then the Levi-foliation extends to a singular codimension one holomorphic foliation of a neighborhood of the hypersurface.
21 pages, minor typos fixed, updated references, accepted to Math. Ann
References in corpus (4)
Cited by in corpus (10)
- Normal forms for CR singular codimension two Levi-flat submanifolds
- CR singular images of generic submanifolds under holomorphic maps
- Dicritical singularities and laminar currents on Levi-flat hypersurfaces
- Singular Levi-flat hypersurfaces in complex projective space induced by curves in the Grassmannian
- Segre-Degenerate Points Form a Semianalytic Set
- Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations
- On Normal Forms for Levi-flat hypersurfaces with an Isolated Line Singularity
- Local normal forms of singular Levi-flat hypersurfaces
- On Segre-degenerate Levi-flat hypervarieties
- Holomorphic foliations tangent to Levi-flat subsets