Special arrangements of lines: codimension two ACM varieties in $\mathbb P^1\times\mathbb P^1\times\mathbb P^1$

TL;DR

This paper characterizes codimension two arithmetically Cohen-Macaulay varieties of lines in the product space P^1×P^1×P^1, providing a combinatorial algebra perspective on their ACM property.

Contribution

It offers a complete characterization of ACM line arrangements in P^1×P^1×P^1 and analyzes their ACM property through combinatorial algebra methods.

Findings

Characterization of codimension two ACM varieties of lines

Description of ACM property via combinatorial algebra

Insight into special line arrangements in multiprojective spaces

Abstract

In this paper we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimensional two arithmetically Cohen-Macaulay (ACM) varieties in $\mathbb P^1\times\mathbb P^1\times\mathbb P^1$, called varieties of lines. We also describe their ACM property from combinatorial algebra point of view.