Pull-back of singular Levi-flat hypersurfaces
Complex Variables
2021-07-06 v1
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 -- Fern\'andez-P\'erez -- Mol.
Keywords
Cite
@article{arxiv.2107.01229,
title = {Pull-back of singular Levi-flat hypersurfaces},
author = {Andrés Beltrán and Arturo Fernández-Pérez and Hernán Neciosup},
journal= {arXiv preprint arXiv:2107.01229},
year = {2021}
}
Comments
Accepted to publication in Arkiv f\"or Matematik