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

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

2006-11-15

arxiv.org/abs/math/0611478v2

Ann. Inst. Fourier, 58 (2008), no. 6, 2037--2073.

Mathematics

Algebraic Geometry

to appear in Annales de l'Institut Fourier

Scientific paper

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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