Type of Work

Article

Date

2015

Journal Title

Journal of Commutative Algebra

Journal ISSN

1939-0807

Journal Volume

7

Journal Issue

2

First Page

189

Last Page

206

DOI

10.1216/JCA-2015-7-2-189

Abstract

We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij-Soederberg 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 [3]. In higher codimension, obstructions arise that inspire our work on an alternative algorithm.

Notes

This document is the publisher's version of an article published in:

Journal of Commutative Algebra, vol. 7, no. 2 (2015): 189-206. doi: 10.1216/JCA-2015-7-2-189

Hamilton Areas of Study

Mathematics