Flasque sheaves on posets and Cohen-Macaulay unions of regular varieties
type: Item
instance of: scholarly article
title: Flasque sheaves on posets and Cohen-Macaulay unions of regular varieties
zbMATH Open document ID: 0681.13012
DOI: 10.1016/0001-8708(89)90058-3
author: Sergey Yuzvinsky
published in: Advances in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The author tries to find new examples of Cohen-Macaulay rings among the coordinate rings of the unions of regular varieties. The method used in this article is to represent a ring as the section ring of a sheaf on a poset. In particular, section \(4\) is devoted to a class of new examples: the generalized face rings. The main result says that the generalized face ring of a simplicial complex K is Cohen-Macaulay if and only if K itself is Cohen-Macaulay.
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 14M05
zbMATH DE Number: 4114767
zbMATH Keywords: seminormality
zbMATH Keywords: poset
zbMATH Keywords: Cohen-Macaulay rings
zbMATH Keywords: section ring of a sheaf
zbMATH Keywords: generalized face ring
MaRDI profile type: Publication
full work available at URL: 0001-8708(89)90058-3
OpenAlex ID: W1978820381
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reviewed by: Masayoshi Nagata
description: scientific article; zbMATH DE number 4114767