The cone of Betti diagrams over a hypersurface ring of low embedding dimension
Christine Berkesch, Jesse Burke, Daniel Erman, Courtney Gibbons
October 2012
Abstract
We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form , where is a homogeneous quadric. We also provide a finite algorithm for decomposing Betti diagrams, including diagrams of infinite projective dimension, into pure diagrams. Boij–Söderberg theory completely describes the cone of Betti diagrams over a standard graded polynomial ring; our result provides the first example of another graded ring for which the cone of Betti diagrams is entirely understood.
Publication
Journal of Pure and Applied Algebra 216 (10), 2256-2268