Toward parametric Cohen-Macaulayfication of two-dimensional finite local cohomology domains
type: Item
instance of: scholarly article
title: Toward parametric Cohen-Macaulayfication of two-dimensional finite local cohomology domains
zbMATH Open document ID: 0714.13017
DOI: 10.1007/BF02571408
published in: Mathematische Zeitschrift
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174289
review text: We show that if (R,\({\mathfrak M})\) is a 2-dimensional local domain having finite local cohomology module \(H^ 1_{{\mathfrak M}}(R)\) (equivalently, R is a 2-dimensional local unmixed domain), and having algebraically closed residue field, such that \({\mathfrak M}^ 2\) is included in \(Ann(H^ 1_{{\mathfrak M}}(R))\), then any sequence of \(\ell +2\) successive parametric blowings-up of R necessarily produces a Cohen-Macaulay scheme, where \(\ell:=[\frac{\ell_ R(H^ 1_{{\mathfrak M}}(R))}{2}]\) (greatest integer). This gives a measure of the ``non-Cohen-Macaulayness'' of the singularity, partially generalizing results of Goto, Schenzel, et al. Some related ideal-theoretic results and some examples are included.
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13H15
zbMATH DE Number: 4175114
zbMATH Keywords: non-Cohen-Macaulayness of singularity
zbMATH Keywords: 2-dimensional local domain
zbMATH Keywords: finite local cohomology module
zbMATH Keywords: blowings-up
author: Bernard L. Johnston
MaRDI profile type: Publication
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OpenAlex ID: W2082749645
description: scientific article; zbMATH DE number 4175114