Tsuchihashi's cusp singularities are Buchsbaum singularities
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.
scientific article; zbMATH DE number 3912510
scientific article