Tsuchihashi's cusp singularities are Buchsbaum singularities
type: Item
instance of: scholarly article
title: Tsuchihashi's cusp singularities are Buchsbaum singularities
zbMATH Open document ID: 0572.14004
author: Masa-Nori Ishida
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1984-01-01T00:00:00Z
review text: A Noetherian local ring \(A\) is said to be Buchsbaum if the difference \(\text{length}(A/I)-\text{mult}(I,A)\), defined for any ideal \(I\) generated by a system of parameters, is independent of \(I\). A Cohen-Macaulay ring is Buchsbaum; in fact, \(A\) is Cohen-Macaulay if and only if the above difference is zero for all \(I\). \textit{H. Tsuchihashi} constructed [Tôhoku Math. J. (2) 35, 607--639 (1983; Zbl 0585.14004)] certain cusp singularities in higher dimensions. These are, in general, not Cohen-Macaulay. In the paper under review the author proves that all these singularities are Buchsbaum. The proof is obtained by determining a suitable truncation of the normalized dualizing complex of the singularity and using a characterization of Buchsbaum singularities given by P. Schenzel.
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 3912510
zbMATH Keywords: Buchsbaum singularities
zbMATH Keywords: Buchsbaum ring
zbMATH Keywords: cusp singularities
reviewed by: Balwant Singh
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228847
OpenAlex ID: W1979396764
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DOI: 10.2748/TMJ/1178228847
description: scientific article; zbMATH DE number 3912510