Classifying ACM sets of points in $P^1XP^1$ via separators

TL;DR

This paper presents a concise proof for classifying ACM sets of points in the product of projective lines, $P^1 imes P^1$, using the concept of separators, advancing understanding in algebraic geometry.

Contribution

It offers a new, shorter proof of the classification of ACM point sets in $P^1 imes P^1$ based on separators, simplifying previous approaches.

Findings

Provides a concise proof of the classification

Clarifies the role of separators in ACM sets

Enhances understanding of algebraic geometry structures

Abstract

The purpose of this note is to give a new, short proof of a classification of ACM sets of points in $P^1XP^1$ in terms of separators.