Hilbert functions and Lefschetz properties for Artinian Gorenstein algebras

Abstract

This work is divided into two parts. In the first one, we studied minimal Hilbert functions for Artinian Gorenstein algebras, we conjecture that for certain algebras the Hilbert vector is always minimal, and prove this conjecture for a particular case. In the second part, we studied the Lefschetz locus for Artinian Gorenstein algebras with Hilbert vector (1, N + 1, N + 1, 1).