Hilbert functions of Artinian Gorenstein algebras with the strong Lefschetz property
| Autor: | Nasrin Altafi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Property (philosophy) General Mathematics strong Lefschetz property Commutative Algebra (math.AC) symbols.namesake Mathematics::Algebraic Geometry FOS: Mathematics Algebra over a field Mathematics Matematik Hilbert series and Hilbert polynomial Mathematics::Commutative Algebra Applied Mathematics Mathematics::History and Overview Mathematics::Rings and Algebras 13E10 13D40 13H10 05E40 SI-sequence Artinian Gorenstein algebra Mathematics - Commutative Algebra If and only if Hilbert function symbols Hessians Macaulay dual generators |
| Zdroj: | Proceedings of the American Mathematical Society. 150:499-513 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/proc/15676 |
| Popis: | We prove that a sequence $h$ of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property if and only if it is an SI-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. Comment: 16 pages; minor revision; to appear in the Proc. of the AMS |
| Databáze: | OpenAIRE |
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