4 problems

Conjecture. Every codimension-one foliation on $X$ either admits a singular transversely projective structure, or is the pull-back, by a rational map, of a foliation on a complex s…

Let $d4d5$ be a codimension one foliation on a compact complex manifold. A foliation is transversely projective when its transverse structure is projective, and $d4d5$ is everywher…

Brunella–Lins Neto conjecture. Either ${\mathcal F}$ is transversely projective on a Zariski-open subset, or there exist a rational map

Consider the double-coset $G$-spaces of the form $K\backslash L/\Gamma$, where $L$ is a semisimple Lie group with an irreducible lattice $\Gamma$ and a compact subgroup $K$, and th…