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MATSUOKA Naoyuki
Department Undergraduate School , School of Science and Technology Position Professor |
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| Language | English |
| Publication Date | 2016/06 |
| Type | Academic Journal |
| Peer Review | Peer reviewed |
| Title | Uniformly Cohen-Macaulay simplicial complexes and almost Gorenstein* simplicial complexes |
| Contribution Type | Co-authored (Other) |
| Journal | Journal of Algebra |
| Journal Type | Another Country |
| Volume, Issue, Page | 455,pp.14-31 |
| Author and coauthor | Naoyuki Matsuoka, Satoshi Murai |
| Details | 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 almostGorenstein* 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. |
| DOI | 10.1016/j.jalgebra.2016.02.005 |
| ISSN | 00218693 |
| PermalinkURL | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84963836263&origin=inward |