Recursive strategy for decomposing Betti tables of complete intersections

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.

References in corpus (1)

• Rational combinations of Betti diagrams of complete intersections

Cited by in corpus (1)

• Syzygies of ${\mathbb{P}}^1\times {\mathbb{P}}^1$: data and conjectures