  Local orbits of a pure state of an N x N bi-partite quantum system are
analyzed. We compute their dimensions which depends on the degeneracy of the
vector of coefficients arising by the Schmidt decomposition. In particular, the
generic orbit has 2N^2 -N-1 dimensions, the set of separable states is 4(N-1)
dimensional, while the manifold of maximally entangled states has N^2-1
dimensions.
