On normality of ASL domains
type: Item
instance of: scholarly article
title: On normality of ASL domains
zbMATH Open document ID: 0624.13019
author: Shiroh Itoh
published in: Hiroshima Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: ASL stands for ``algebra with straightening laws'' in the sense of \textit{D. Eisenbud} [in Ring theory and algebra III, Proc. 3rd Okla. Conf., 1979, Lect. Notes Pure Appl. Math. 55, 243-268 (1980; Zbl 0448.13010)], alias ordinal Hodge algebra. The author gives some sufficient conditions for a graded ASL on a poset H over a field k to be a normal domain, assuming that the associated discrete ASL, k[H], is Cohen-Macaulay and that all maximal chains in H have the same length. His conditions are too technical to write here, but the arithmetic normality of Grassmann and Schubert varieties is easily derived from them. The key observation is that \textit{bad} prime ideals of height one of k[H] correspond with special subsets of H which he calls \textit{spindles} of H.
reviewed by: H.Matsumura
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 4012785
zbMATH Keywords: ASL
zbMATH Keywords: algebra with straightening laws
zbMATH Keywords: Hodge algebra
zbMATH Keywords: normality
zbMATH Keywords: Schubert varieties
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4012785