Non-normal \({\mathcal D}\)-affine varieties with injective normalisation
type: Item
instance of: scholarly article
title: Non-normal \({\mathcal D}\)-affine varieties with injective normalisation
zbMATH Open document ID: 0839.13017
author: A. G. Jones
published in: Journal of Algebra
publication date: 1996-06-19T00:00:00Z
review text: This paper uses similar techniques as the author's paper reviewed above [ibid. 180-199 (1995; see the preceding review)]. The main result is the following: Let \({\mathcal H}\) be a Cohen-Macaulay monomial variety with normalisation \(\mathbb{P}^r_k (m,1, \dots, 1)\) for some \(m \geq 1\) [weighted projective space] and injective normalization map. Then the rings of differential operators on \({\mathcal H}\) and \(\mathbb{P}^r_k (m,1, \dots,1)\) are Morita-equivalent iff \(H^r ({\mathcal H}, {\mathcal O}_{\mathcal H}) = 0\) or iff \(H^i ({\mathcal H}, {\mathcal O}_{\mathcal H}) = 0\) for all \(i > 0\) or iff \({\mathcal H}\) is \({\mathcal D}\)-affine (cf. definition 2.5 of the paper under review). This result is used to construct nonnormal \({\mathcal D}\)-affine varieties with injective normalisation such that the normalization is not regular.
Mathematics Subject Classification ID: 13N10
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 16W25
zbMATH DE Number: 763941
zbMATH Keywords: Morita equivalence
zbMATH Keywords: Cohen-Macaulay monomial variety
zbMATH Keywords: rings of differential operators
reviewed by: Karl-Heinz Kiyek
MaRDI profile type: Publication
Wikidata QID: Q122947001
full work available at URL: jabr.1995.1084
OpenAlex ID: W2093642263
DOI: 10.1006/JABR.1995.1084
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description: scientific article; zbMATH DE number 763941