Explicit projective embeddings of standard opens of the Hilbert scheme   of points
  We describe explicitly how certain standard opens of the Hilbert scheme of points are embedded into Grassmannians. The standard opens of the Hilbert scheme that we consider are given as the intersection of a corresponding basic open affine of the Grassmannian and a closed stratum determined by a Fitting ideal. 
Roy Mikael Skjelnes, Gustav S{\ae}d\'en St{\aa}hl
math.AG