Hilbert functions of Gorenstein algebras with Lefschetz properties

Abstract: In 1995 T. Harima characterized Hilbert functions of Artinian Gorenstein algebras with the weak Lefschetz property and proved that they are, in fact, Stanley–Iarrobino (SI)- sequences. In this talk, I will generalize T. Harima’s result and prove that SI-sequences classify the Hilbert functions of Artinian Gorenstein algebras with the strong Lefschetz property. The proof uses the Hessian criterion by T. Maeno and J. Watanabe. Using this criterion, I will also provide classes of Artinian Gorenstein algebras of codimension three satisfying the strong Lefschetz property.

commutative algebraalgebraic geometrycombinatoricsrings and algebrasrepresentation theory

Audience: researchers in the topic

Geometry, Algebra, Singularities, and Combinatorics

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