Open Access
SUMMER 2015 Non-simplicial decompositions of Betti diagrams of complete intersections
Courtney Gibbons, Jack Jeffries, Sarah Mayes, Claudiu Raicu, Branden Stone, Bryan White
J. Commut. Algebra 7(2): 189-206 (SUMMER 2015). DOI: 10.1216/JCA-2015-7-2-189


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.


Download Citation

Courtney Gibbons. Jack Jeffries. Sarah Mayes. Claudiu Raicu. Branden Stone. Bryan White. "Non-simplicial decompositions of Betti diagrams of complete intersections." J. Commut. Algebra 7 (2) 189 - 206, SUMMER 2015.


Published: SUMMER 2015
First available in Project Euclid: 14 July 2015

zbMATH: 1327.13048
MathSciNet: MR3370483
Digital Object Identifier: 10.1216/JCA-2015-7-2-189

Primary: 13D02
Secondary: 13C99

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

Vol.7 • No. 2 • SUMMER 2015
Back to Top