Unimodal Gorenstein h-vectors without the Stanley–Iarrobino property

Document Type

Article

Publication Date

10-20-2017

Abstract

The study of the h-vectors of graded Gorenstein algebras is an important topic in combinatorial commutative algebra, which despite the large amount of literature produced during the last several years, still presents many interesting open questions. In this note, we commence a study of those unimodal Gorenstein h-vectors that do not satisfy the Stanley–Iarrobino property. Our main results, which are characteristic free, show that such h-vectors exist: 1) In socle degree e if and only if e≥6; and 2) in every codimension five or greater. The main case that remains open is that of codimension four, where no Gorenstein h-vector is known without the Stanley–Iarrobino property. We conclude by proposing the following very general conjecture: The existence of any arbitrary level h-vector is independent of the characteristic of the base field.

Publisher's Statement

Copyright 2017 Taylor & Francis. Publisher’s version of record: https://doi.org/10.1080/00927872.2017.1372457

Publication Title

Communications in Algebra

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