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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
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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