Hilbert functions of Artinian Gorenstein algebras with the strong Lefschetz property
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Abstract:
We prove that a sequence $h$ of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property (SLP) if and only if it is an Stanley-Iarrobino-sequence. This generalizes the result by T. Harima which characterizes the Hilbert functions of Artinian Gorenstein algebras with the weak Lefschetz property. We also provide classes of Artinian Gorenstein algebras obtained from the ideal of points in $\mathbb {P}^n$ such that some of their higher Hessians have non-vanishing determinants. Consequently, we provide families of such algebras satisfying the SLP.References
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Additional Information
- Nasrin Altafi
- Affiliation: Department of Mathematics, KTH Royal Institute of Technology, S-100 44 Stockholm, Sweden
- MR Author ID: 1202673
- Email: nasrinar@kth.se
- Received by editor(s): November 19, 2020
- Received by editor(s) in revised form: May 5, 2021
- Published electronically: November 4, 2021
- Additional Notes: This work was supported by the grant VR2013-4545.
- Communicated by: Claudia Polini
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 499-513
- MSC (2020): Primary 13E10, 13D40, 13H10, 05E40
- DOI: https://doi.org/10.1090/proc/15676
- MathSciNet review: 4356163