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

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

2011-09-23

arxiv.org/abs/1109.5198v2

Mathematics

Commutative Algebra

Minor edits, references updated

Scientific paper

We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form k[x,y]/, 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.

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