  We prove that, for m greater than 3 and k greater than m-2, the Grassmannian
of m-dimensional subspaces of the space of skew-symmetric forms over a vector
space of dimension 2k is birational to the Hilbert scheme of Palatini scrolls
in P^(2k-1).
  For m=3 and k greater than 3, this Grassmannian is proved to be birational to
the set of pairs (E,Y), where Y is a smooth plane curve of degree k and E is a
stable rank-2 bundle on Y whose determinant is O(k-1).
