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Codimension 3 Arithmetically Gorenstein Subschemes of projective $N$-space

R. Hartshorne·I. Sabadini·E. Schlesinger
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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 $n \geq 56$ 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 $\mathbb{P}^3$.

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R. Hartshorne, I. Sabadini, E. Schlesinger. 2008-02-28. Codimension 3 Arithmetically Gorenstein Subschemes of projective $N$-space. https://arxiv.org/abs/math/0611478

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