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VOL. 65 | 2015 Gorenstein in codimension 4: the general structure theory
Miles Reid

Editor(s) Jungkai Alfred Chen, Meng Chen, Yujiro Kawamata, JongHae Keum

## Abstract

I describe the projective resolution of a codimension 4 Gorenstein ideal, aiming to extend Buchsbaum and Eisenbud's famous result in codimension 3. The main result is a structure theorem stating that the ideal is determined by its $(k + 1) \times 2k$ matrix of first syzygies, viewed as a morphism from the ambient regular space to the Spin-Hom variety $\mathrm{SpH}_k \subset \mathrm{Mat}(k + 1, 2k)$. This is a general result encapsulating some theoretical aspects of the problem, but, as it stands, is still some way from tractable applications.

## Information

Published: 1 January 2015
First available in Project Euclid: 19 October 2018

zbMATH: 1360.13036
MathSciNet: MR3380790

Digital Object Identifier: 10.2969/aspm/06510201

Subjects:
Primary: 13D25, 13H10
Secondary: 13D02, 14J10, 14M05