Suppose that M is a finitely generated module over A=k[X_1,...,X_n] of Krull dimension m with k an infinite field. Then one version of Noether normalisation says there is an m-dimensional k-subspace W of the k-vector space spanned by X_1,...,X_n such that M is finitely generated over Sym(W) considered as a subring of A.

As is surely well-known, in fact one can show that the set of m-dimensional k-vector spaces W that work is open in the appropriate Grassmannian. My question is where is there a reference for this fact in the literature?