Chow's theorem for real analytic Levi-flat hypersurfaces

Arturo Fernández-Pérez, Rogério Mol, Rudy Rosas

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

Resumen

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.

Idioma originalInglés
Número de artículo103169
PublicaciónBulletin des Sciences Mathematiques
Volumen179
DOI
EstadoPublicada - oct. 2022

Huella

Profundice en los temas de investigación de 'Chow's theorem for real analytic Levi-flat hypersurfaces'. En conjunto forman una huella única.

Citar esto