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Chow's theorem for real analytic Levi-flat hypersurfaces.
- Source :
-
Bulletin des Sciences Mathematiques . Oct2022, Vol. 179, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- In this article we provide a version of Chow's theorem for real analytic Levi-flat hypersurfaces in the complex projective space P n , n ≥ 2. More specifically, we prove that a real analytic Levi-flat hypersurface M ⊂ P n , with singular set of real dimension at most 2 n − 4 and whose Levi leaves are contained in algebraic hypersurfaces, is tangent to the levels of a rational function in P n. As a consequence, M is a semialgebraic set. We also prove that a Levi foliation on P n — a singular real analytic foliation whose leaves are immersed complex manifolds of codimension one — satisfying similar conditions — singular set of real dimension at most 2 n − 4 and all leaves algebraic — is defined by the level sets of a rational function. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00074497
- Volume :
- 179
- Database :
- Academic Search Index
- Journal :
- Bulletin des Sciences Mathematiques
- Publication Type :
- Academic Journal
- Accession number :
- 158745914
- Full Text :
- https://doi.org/10.1016/j.bulsci.2022.103169