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

Christine Berkesch, Jesse Burke, Daniel Erman, Courtney Gibbons

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2256-2268
Number of pages13
JournalJournal of Pure and Applied Algebra
Volume216
Issue number10
DOIs
StatePublished - Oct 2012
Externally publishedYes

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