Castelnuovo-Mumford regularity and arithmetic Cohen-Macaulayness of complete bipartite subspace arrangements

TL;DR

This paper determines the Castelnuovo-Mumford regularity and conditions for arithmetic Cohen-Macaulayness of certain complete bipartite subspace arrangements in projective space.

Contribution

It provides explicit regularity formulas and characterizes when these arrangements are arithmetically Cohen-Macaulay, extending understanding of their algebraic properties.

Findings

Regularity formula for arrangements with large bipartite graphs

Criteria for arithmetic Cohen-Macaulayness of these arrangements

Identification of specific arrangements satisfying Cohen-Macaulay property

Abstract

We give the Castelnuovo-Mumford regularity of arrangements of (n-2)-planes in P^n whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen-Macaulay.