Recursive strategy for decomposing Betti tables of complete intersections

TL;DR

This paper presents a recursive algorithm for decomposing Betti tables of complete intersections, enabling analysis of their Boij-Soederberg decompositions and stability properties, especially for codimension four cases with large degrees.

Contribution

It introduces a new recursive decomposition method for Betti diagrams of complete intersections, facilitating the study of their Boij-Soederberg decompositions and stability.

Findings

The recursive algorithm effectively decomposes Betti tables of complete intersections.

The method produces Boij-Soederberg decompositions when the largest degree is sufficiently large.

Detailed analysis provided for codimension four complete intersections with large degrees.

Abstract

We introduce a recursive decomposition algorithm for the Betti diagram of a complete intersection using the diagram of a complete intersection defined by a subset of the original generators. This alternative algorithm is the main tool that we use to investigate stability and compatibility of the Boij-Soederberg decompositions of related diagrams; indeed, when the biggest generating degree is sufficiently large, the alternative algorithm produces the Boij-Soederberg decomposition. We also provide a detailed analysis of the Boij-Soederberg decomposition for Betti diagrams of codimension four complete intersections where the largest generating degree satisfies the size condition.