We study the lowest dimensional open case of the question whether every
arithmetically Cohen--Macaulay subscheme of PN is glicci, that is,
whether every zero-scheme in P3 is glicci. We show that a set of n≥56 points in general position in \PP^3 admits no strictly descending
Gorenstein liaison or biliaison. In order to prove this theorem, we establish a
number of important results about arithmetically Gorenstein zero-schemes in
P3.Comment: to appear in Annales de l'Institut Fourie