Rational combinations of Betti diagrams of complete intersections

TL;DR

This paper explores whether Betti diagrams of modules over polynomial rings can be decomposed into sums of Betti diagrams of complete intersections, using Boij-S"oderberg theory and cone analysis.

Contribution

It identifies extremal rays of the cone generated by complete intersection Betti diagrams and proposes an initial algorithm for their decomposition.

Findings

Characterized extremal rays of the cone of complete intersection Betti diagrams

Developed a basic algorithm for decomposing Betti diagrams

Provided insights into the structure of Betti diagrams within Boij-S"oderberg theory

Abstract

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 determine if it is possible to decompose it into the Betti diagrams of complete intersections. To do so, we determine the extremal rays of the cone generated by the diagrams of complete intersections and provide a rudimentary algorithm for decomposition.