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]/<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--Soederberg 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.

Minor edits, references updated

References in corpus (1)

• Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case

Cited by in corpus (6)

• Categorified duality in Boij-Söderberg Theory and invariants of free complexes
• The cone of Betti tables over a rational normal curve
• The cone of Betti tables over three non-collinear points in the plane
• Towards Boij-Söderberg theory for Grassmannians: the case of square matrices
• Foundations of Boij-Söderberg Theory for Grassmannians
• Questions about Boij-Söderberg theory