Betti tables forcing failure of the Weak Lefschetz Property
Speaker:
Sean Grate, Auburn University
Date and Time:
Thursday, May 18, 2023 - 9:45am to 10:30am
Location:
Fields Institute, Room 230
Abstract:
We study the Artinian reduction $A$ of a configuration of a pointset $X$ $\subseteq$ ¶$^{n}$, 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.