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.
Citation Information
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.
https://digitalcommons.hamilton.edu/articles/58
Hamilton Areas of Study
Mathematics
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