Unique maximal Betti diagrams for Artinian Gorenstein k-algebras with the weak Lefschetz property

Abstract

We give an alternate proof for a theorem of Migliore and Nagel. In particular, we show that if $\mathcal{H}$ is an SI-sequence, then the collection of Betti diagrams for all Artinian Gorenstein k-algebras with the weak Lefschetz property and Hilbert function $\mathcal{H}$ has a unique largest element.

KEYWORDS:

• Artinian Gorenstein k-algebras
• Graded Betti numbers
• Hilbert functions

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13D02
• 13H10