Journal of Commutative Algebra

Non-simplicial decompositions of Betti diagrams of complete intersections

Courtney Gibbons, Jack Jeffries, Sarah Mayes, Claudiu Raicu, Branden Stone, and Bryan White

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We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij-S\"oderberg theory. That is, given a Betti diagram, we decompose it into pure diagrams. Relaxing the requirement that the degree sequences in such pure diagrams be totally ordered, we are able to define a multiplication law for Betti diagrams that respects the decomposition and allows us to write a simple expression of the decomposition of the Betti diagram of any complete intersection in terms of the degrees of its minimal generators. In the more traditional sense, the decomposition of complete intersections of codimension at most 3 are also computed as given by the totally ordered decomposition algorithm obtained from \cite{ES1}. In higher codimension, obstructions arise that inspire our work on an alternative algorithm.

Article information

J. Commut. Algebra Volume 7, Number 2 (2015), 189-206.

First available in Project Euclid: 14 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13C99: None of the above, but in this section


Gibbons, Courtney; Jeffries, Jack; Mayes, Sarah; Raicu, Claudiu; Stone, Branden; White, Bryan. Non-simplicial decompositions of Betti diagrams of complete intersections. J. Commut. Algebra 7 (2015), no. 2, 189--206. doi:10.1216/JCA-2015-7-2-189.

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