Article Title

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

Type of Work

Article

Date

2012

Journal Title

Journal of Pure and Applied Algebra

Journal ISSN

0022-4049

Journal Volume

216

Journal Issue

10

First Page

2256

Last Page

2268

DOI

10.1016/j.jpaa.2012.03.007

Abstract

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.

Notes

This page links to a version of the paper posted at arXiv.org on February 20, 2012.

The article was published in:
Journal of Pure and Applied Algebra, vol. 216, no. 10 (2012): 2256-2268. doi: 10.1016/j.jpaa.2012.03.007

Hamilton Areas of Study

Mathematics