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

2010/11/11 by Sumi Seo, Seo, Sumi, Hema Srinivasan +1 · 1 citation
Mathematics · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1011.2732

Abstract

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, h₄,...), where h₄≤ 34 are unimodal. Combining this with the previously known results, we obtain that all Gorenstein h-vectors (1, h₁, h₂,h₃, h₄, ....) are unimodal if h₄≤ 3.

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