Codimension 3 Arithmetically Gorenstein Subschemes of projective N-space

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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 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.