Gorenstein in codimension 4 - the general structure theory

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) x 2k matrix of first syzygies, viewed as a morphism from the ambient regular space to the Spin-Hom variety SpH_k in 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.

To appear in Algebraic Geometry in East Asia (Taipei Nov 2011), Advanced Studies in Pure Mathematics, 2013. 30 pp, The website http://www.warwick.ac.uk/staff/Miles.Reid/codim4 contains material accompanying this paper