Uniformly Cohen-Macaulay simplicial complexes and almost Gorenstein* simplicial complexes

Naoyuki Matsuoka, Satoshi Murai

研究成果: Article査読

3 被引用数 (Scopus)

抄録

In this paper, we study simplicial complexes whose Stanley-Reisner rings are almost Gorenstein and have a-invariant zero. We call such a simplicial complex an almost Gorenstein* simplicial complex. To study the almost Gorenstein* property, we introduce a new class of simplicial complexes which we call uniformly Cohen-Macaulay simplicial complexes. A d-dimensional simplicial complex δ is said to be uniformly Cohen-Macaulay if it is Cohen-Macaulay and, for any facet F of δ, the simplicial complex δ\ (F) is Cohen-Macaulay of dimension d. We investigate fundamental algebraic, combinatorial and topological properties of these simplicial complexes, and show that almost Gorenstein* simplicial complexes must be uniformly Cohen-Macaulay. By using this fact, we show that every almost Gorenstein* simplicial complex can be decomposed into those of having one dimensional top homology. Also, we give a combinatorial criterion of the almost Gorenstein* property for simplicial complexes of dimension ≤2.

本文言語English
ページ(範囲)14-31
ページ数18
ジャーナルJournal of Algebra
455
DOI
出版ステータスPublished - 2016 6 1
外部発表はい

ASJC Scopus subject areas

  • Algebra and Number Theory

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