We construct a space GXnβ and a rank n, generically etale family of
closed subspaces in a separated ambient space X. The constructed pair
satisfies a universal property of generically etale families of closed
subspaces in X. This universal property is derived directly from the
construction and does in particular not use the Hilbert scheme. The constructed
space GXnβ is by its universal property canonically identified with a closed
subspace of the Hilbert scheme.Comment: 28 pages; replaced TSnβ1RβR with TSnβ1,1R;
simplified some proof