
I discuss some practical constructions of Gorenstein rings in codimension 4, and my attempt to give a general structure theory based on Spin-Hom varieties, that should serve as key varieties for first syzygies.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/4280