On the fattening of ACM arrangements of codimension 2 subspaces in P^N

TL;DR

This paper investigates configurations of codimension 2 subspaces in projective spaces, classifying those with minimal growth rates of their initial sequences, extending previous work to higher dimensions.

Contribution

It generalizes prior classifications of ACM arrangements of codimension 2 subspaces to projective spaces of any dimension.

Findings

Classified ACM arrangements with minimal initial sequence growth in P^N

Extended known results from P^2 and P^3 to arbitrary dimensions

Provided a framework for understanding growth rates in higher-dimensional configurations

Abstract

In the present note we study configurations of codimension 2 flats in projective spaces and classify those with the smallest rate of growth of the initial sequence. Our work extends those of Bocci, Chiantini in P^2 and Janssen in P^3 to projective spaces of arbitrary dimension.