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arXiv · 1109.5198

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

Christine Berkesch·Jesse Burke·Daniel Erman·Courtney Gibbons
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Abstract

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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Christine Berkesch, Jesse Burke, Daniel Erman, Courtney Gibbons. 2012-02-20. The cone of Betti diagrams over a hypersurface ring of low embedding dimension. https://doi.org/10.1016/j.jpaa.2012.03.007

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