Hilbert functions and set of points in $\mathbb P^1\times \mathbb P^1$

TL;DR

This paper characterizes a class of matrices that can serve as Hilbert functions for 0-dimensional schemes in the product of two projective lines, advancing understanding of algebraic geometry in this setting.

Contribution

It identifies and characterizes admissible matrices that correspond to Hilbert functions of 0-dimensional schemes in b^1b^1, providing a classification framework.

Findings

Identified a class of admissible matrices for Hilbert functions.

Established criteria for matrices to correspond to 0-dimensional schemes.

Enhanced understanding of Hilbert functions in b^1b^1.

Abstract

In this paper we determine a class of admissible matrices which are the Hilbert functions of some 0-dimensional schemes in $\mathbb P^1\times\mathbb P^1$.