Arkiv för Matematik
Volume 59 (2021)
Pull-back of singular Levi-flat hypersurfaces
Pages: 307 – 321
We study singular real analytic Levi-flat subsets invariant by singular holomorphic foliations in complex projective spaces. We give sufficient conditions for a real analytic Levi-flat subset to be the pull-back of a semianalytic Levi-flat hypersurface in a complex projective surface under a rational map or to be the pull-back of a real algebraic curve under a meromorphic function. In particular, we give an application to the case of a singular real analytic Levi-flat hypersurface. Our results improve previous ones due to Lebl and Bretas–Fernández-Pérez–Mol.
Levi-flat subsets, holomorphic foliations
2010 Mathematics Subject Classification
This work was supported by the Pontifícia Universidad Católica del Perú project VRIDGI-2018-0024. The second author is partially supported by CNPq-Brazil Grant Number 302790/2019-5.
Received 16 June 2020
Accepted 5 May 2021
Published 11 November 2021