The Hilbert function of bigraded algebras in $k[\mathbb{P}^1\times\mathbb{P}^1]$

TL;DR

This paper classifies the Hilbert functions of bigraded algebras in a specific polynomial ring using a new numerical tool called Ferrers function, advancing understanding of algebraic structures in biprojective spaces.

Contribution

It introduces Ferrers functions as a novel method to classify Hilbert functions of bigraded algebras in $k[P^1 imes P^1]$, providing a systematic approach.

Findings

Classification of Hilbert functions achieved

Introduction of Ferrers functions as a classification tool

Enhanced understanding of bigraded algebra structures

Abstract

We classify the Hilbert functions of bigraded algebras in $k[x_1, x_2, y_1, y_2]$ introducing a numerical function called Ferrers function.