On Unimodality of Hilbert Functions of Gorenstein Artin Algebras of Embedding Dimension Four

Details On Unimodality of Hilbert Functions of Gorenstein Artin Algebras of Embedding Dimension Four On Unimodality of Hilbert Functions of Gorenstein Artin Algebras of Embedding Dimension Four

2010-11-11

arxiv.org/abs/1011.2732v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

We prove that the Hilbert functions of codimension four graded Gorenstein Artin algebras R/I are unimodal provided I has a minimal generator in degree less than five. It is an open question whether all Gorenstein h-vectors in codimension four are unimodal. In this paper, we prove that Hilbert functions of all artinian codimension four Gorenstein algebras starting with (1,4,10, 20, h_4,...), where h_4\leq 34 are unimodal. Combining this with the previously known results, we obtain that all Gorenstein h-vectors (1, h_1, h_2,h_3, h_4, ....) are unimodal if h_4\leq 3.

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