TY - JOUR

T1 - Chow's theorem for real analytic Levi-flat hypersurfaces

AU - Fernández-Pérez, Arturo

AU - Mol, Rogério

AU - Rosas, Rudy

N1 - Publisher Copyright:
© 2022 Elsevier Masson SAS

PY - 2022/10

Y1 - 2022/10

N2 - In this article we provide a version of Chow's theorem for real analytic Levi-flat hypersurfaces in the complex projective space Pn, n≥2. More specifically, we prove that a real analytic Levi-flat hypersurface M⊂Pn, with singular set of real dimension at most 2n−4 and whose Levi leaves are contained in algebraic hypersurfaces, is tangent to the levels of a rational function in Pn. As a consequence, M is a semialgebraic set. We also prove that a Levi foliation on Pn — a singular real analytic foliation whose leaves are immersed complex manifolds of codimension one — satisfying similar conditions — singular set of real dimension at most 2n−4 and all leaves algebraic — is defined by the level sets of a rational function.

AB - In this article we provide a version of Chow's theorem for real analytic Levi-flat hypersurfaces in the complex projective space Pn, n≥2. More specifically, we prove that a real analytic Levi-flat hypersurface M⊂Pn, with singular set of real dimension at most 2n−4 and whose Levi leaves are contained in algebraic hypersurfaces, is tangent to the levels of a rational function in Pn. As a consequence, M is a semialgebraic set. We also prove that a Levi foliation on Pn — a singular real analytic foliation whose leaves are immersed complex manifolds of codimension one — satisfying similar conditions — singular set of real dimension at most 2n−4 and all leaves algebraic — is defined by the level sets of a rational function.

KW - CR-manifold

KW - Holomorphic foliation

KW - Levi-flat variety

UR - http://www.scopus.com/inward/record.url?scp=85134190653&partnerID=8YFLogxK

U2 - 10.1016/j.bulsci.2022.103169

DO - 10.1016/j.bulsci.2022.103169

M3 - Article

AN - SCOPUS:85134190653

SN - 0007-4497

VL - 179

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

M1 - 103169

ER -