Betti tables forcing failure of the Weak Lefschetz Property
We study the Artinian reduction A of a configuration of a pointset X ⊆ ¶n, and the relation of the geometry of X to Lefschetz properties of A. Migliore-Zanello initiated the study of this connection, with a particular focus on the Hilbert function of A, and further work appears in Migliore-Miró-Roig–Nagel. Our specific focus is on betti tables rather than Hilbert functions, and we prove that certain betti tables force the failure of theWeak Lefschetz Property (WLP); the corresponding Artinian algebras are typically not level, and the failure of WLP is not detected in terms of the Hilbert function.