## Advanced Studies in Pure Mathematics

### Gorenstein in codimension 4: the general structure theory

Miles Reid

#### 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.

#### Article information

Dates
Revised: 25 February 2013
First available in Project Euclid: 19 October 2018

https://projecteuclid.org/ euclid.aspm/1539916454

Digital Object Identifier
doi:10.2969/aspm/06510201

Mathematical Reviews number (MathSciNet)
MR3380790

Zentralblatt MATH identifier
1360.13036

#### Citation

Reid, Miles. Gorenstein in codimension 4: the general structure theory. Algebraic Geometry in East Asia — Taipei 2011, 201--227, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06510201. https://projecteuclid.org/euclid.aspm/1539916454