Families of artinian and low dimensional determinantal rings

In this paper we extend previous results on the dimension and codimension of Ws(b_;a_) in GradAlg(H) to artinian determinantal rings, and we show that GradAlg(H) is generically smooth along Ws(b_;a_) under some assumptions. For zero and one dimensional determinantal schemes we generalize earlier results on these questions. As a consequence we get that the general element of a component W of the Hilbert scheme of Pn is glicci provided W contains a standard determinantal scheme satisfying some conditions. We also show how certain ghost terms disappear under deformation while other ghost terms remain and are present in the minimal resolution of a general element of GradAlg(H).