Pull-back of singular levi-flat hypersurfaces

We study singular real analyti Levi-flat subsets invariant by singular holo-morphi foliations in omplex projetive spaes. We give suffiient onditions for a real analyti Levi-flat subset to be the pull-bak of a semianalyti Levi-flat hypersurfae in a omplex projetive surfae under a rational map or to be the pull-bak of a real algebrai urve under a meromorphi funtion. In partiular, we give an appliation to the ase of a singular real analyti Levi-flat hypersurfae. Our results improve previous ones due to Lebl and Bretas–Fernández-Pérez–Mol.