The cone of Betti diagrams over a hypersurface ring of low embedding dimension
Type of Work
Journal of Pure and Applied Algebra
We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form k[x,y]/⟨q⟩, where q 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.
Gibbons, Courtney; Burke, Jesse; Erman, Daniel; and Berkesch, Christine, "The cone of Betti diagrams over a hypersurface ring of low embedding dimension" (2012). Hamilton Digital Commons.
Hamilton Areas of Study