A classification of the weak Lefschetz property for almost complete intersections generated by uniform powers of general linear forms

Boij, Mats; Lundqvist, Samuel

doi:10.2140/ant.2023.17.111

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A classification of the weak Lefschetz property for almost complete intersections generated by uniform powers of general linear forms

Mats Boij and Samuel Lundqvist

Vol. 17 (2023), No. 1, 111–126

DOI: 10.2140/ant.2023.17.111

Abstract

We use Macaulay’s inverse system to study the Hilbert series for almost complete intersections generated by uniform powers of general linear forms. This allows us to give a classification of the weak Lefschetz property for these algebras, settling a conjecture by Migliore, Miró-Roig, and Nagel.

Keywords

powers of linear forms, general linear forms, almost complete intersections, weak Lefschetz property, inverse system, Hilbert series

Mathematical Subject Classification

Primary: 13E10

Secondary: 13C13, 13C40, 13D40

Milestones

Received: 24 June 2021

Revised: 16 January 2022

Accepted: 17 March 2022

Published: 24 March 2023

Authors

Mats Boij
Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden

Samuel Lundqvist
Department of Mathematics Stockholm University Stockholm Sweden

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Vol. 17, No. 1, 2023