Betti numbers of fold products of linear forms

TL;DR

This paper investigates the Betti numbers of ideals generated by fold products of linear forms, extending previous work on their linear resolutions to a deeper homological analysis.

Contribution

It advances the understanding of the homological properties of fold product ideals, building on prior results about their linear resolutions.

Findings

Betti numbers of fold product ideals are characterized.

These ideals have linear graded free resolutions.

The study provides new insights into their homological structure.

Abstract

The ideals generated by fold products of linear forms are generalizations of powers of defining ideals of star configurations, or of Veronese type ideals, and in this paper we study their Betti numbers. In earlier work, the authors together with Yu Xie showed that these ideals have linear graded free resolution, and in this paper we take the study of the homological information about these ideals to the next natural level.