Cerveau–Lins Neto's transverse-projectivity conjecture for compact complex foliations

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 everywhere tangent to a foliation by codimension two compact subvarieties when its tangent directions are contained in those of such a foliation. Cerveau–Lins Neto's conjecture. Every codimension one foliation on a compact complex manifold either is transversely projective or is everywhere tangent to a foliation by codimension two compact subvarieties. This is presented as a stronger version of Brunella's conjecture; the supplied text gives no resolution, so its general status remains open.