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 ${\mathbb{P}}^N$ is glicci, that is, whether every zero-scheme in ${\mathbb{P}}^3$ is glicci. We show that a set of $n\ge 56$ 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 ${\mathbb{P}}^3$.

to appear in Annales de l'Institut Fourier