Hilbert Functions Of Artinian Gorenstein Algebras With The Strong Lefschetz Property

• 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 P-n such that some of their higher Hessians have non-vanishing determinants. Consequently, we provide families of such algebras satisfying the SLP.

Ämnesord

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Nyckelord

Artinian Gorenstein algebra

Hilbert function

Hessians

Macaulay dual generators

strong Lefschetz property

SI-sequence

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