Arkiv för Matematik

Volume 59 (2021)

Number 2

Pull-back of singular Levi-flat hypersurfaces

Pages: 307 – 321

DOI: https://dx.doi.org/10.4310/ARKIV.2021.v59.n2.a3

Authors

Andrés Beltrán (Dpto. Ciencias, Sección Matemáticas, Pontifícia Universidad Católica del Perú, Lima, Peru)

Arturo Fernández-Pérez (Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil)

Hernán Neciosup (Dpto. Ciencias, Sección Matemáticas, Pontifícia Universidad Católica del Perú, Lima, Peru)

Abstract

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.

Keywords

Levi-flat subsets, holomorphic foliations

2010 Mathematics Subject Classification

32S65, 32V40

Full Text (PDF format)

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