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Summer 2021 Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections
David Cook II, Uwe Nagel
J. Commut. Algebra 13(2): 157-178 (Summer 2021). DOI: 10.1216/jca.2021.13.157

Abstract

Deciding the presence of the weak Lefschetz property often is a challenging problem. Continuing studies of Brenner and Kaid (2007), Cook II and Nagel (2011) and Migliore, Miró-Roig, Murai and Nagel (2013) we carry out an in-depth study of Artinian monomial ideals with four generators in three variables. We use a connection to lozenge tilings to describe semistability of the syzygy bundle of such an ideal, to determine its generic splitting type, and to decide the presence of the weak Lefschetz property. We provide results in both characteristic zero and positive characteristic.

Citation

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David Cook II. Uwe Nagel. "Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections." J. Commut. Algebra 13 (2) 157 - 178, Summer 2021. https://doi.org/10.1216/jca.2021.13.157

Information

Received: 17 September 2016; Revised: 30 November 2018; Accepted: 9 December 2018; Published: Summer 2021
First available in Project Euclid: 30 June 2021

Digital Object Identifier: 10.1216/jca.2021.13.157

Subjects:
Primary: 05A15
Secondary: 05B45, 13E10

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.13 • No. 2 • Summer 2021
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