The cone of Betti diagrams over a hypersurface ring of low embedding dimension

Abstract

We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form $k [x, y]/\langle q \rangle$, 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. Boijâ€“SÃ¶derberg 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.

Type
Publication
Journal of Pure and Applied Algebra 216 (10), 2256-2268