On the question of the point correspondences between three projective spaces

Point correspondences between three projective spaces, studied by M. Villa, are considered in one- and $n$-dimensional cases. Trilinear correspondences between three projective lines are classified. Some properties of the bundle of trilinear correspondences osculating to a general correspondence of three lines are given. Analogous properties of osculating generalized Godeaux correspondences are studied in the $n$-dimensional case.