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

Giuseppe Favacchio

doi:10.1216/jca.2020.12.479

Abstract

We classify the Hilbert functions of bigraded algebras in $k [x_{1}, x_{2}, y_{1}, y_{2}]$ by introducing a numerical function called a Ferrers function.

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Giuseppe Favacchio. "The Hilbert function of bigraded algebras in $k[\mathbb{P}^1 \times \mathbb{P}^1]$." J. Commut. Algebra 12 (4) 479 - 487, Winter 2020. https://doi.org/10.1216/jca.2020.12.479

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Received: 6 October 2016; Revised: 19 May 2017; Accepted: 5 January 2018; Published: Winter 2020

First available in Project Euclid: 5 January 2021

MathSciNet: MR4194937

Digital Object Identifier: 10.1216/jca.2020.12.479

Subjects:

Primary: 13F20

Secondary: 13A15 , 13D40

Keywords: Hilbert function , multigraded algebra , numerical function

Abstract

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