Codimension 3 arithmetically gorenstein subschemes of projective n-space

Abstract

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 general set of n ≥ 56 points in ℙ3 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.