On two-dimensional quasihomogeneous isolated singularities. II
type: Item
instance of: scholarly article
title: On two-dimensional quasihomogeneous isolated singularities. II
zbMATH Open document ID: 0811.14002
DOI: 10.1007/BF01194847
author: Jürgen Herzog
published in: Archiv der Mathematik
publication date: 1995-05-08T00:00:00Z
review text: [For part I see \textit{A. Martsinkovsky}, ibid. 550-555 (1992; Zbl 0792.14003).] This article deals with the following conjecture of Auslander: An analytic two-dimensional isolated singularity \((R,{\mathfrak m},k)\) is quasihomogeneous if and only if the Auslander-module \(A\) of this singularity is isomorphic to the module of Zariski differentials. -- Recall that the Auslander-module is the unique non-trivial extension of the maximal ideal \({\mathfrak m}\) by the canonical module of \(R\), while the module of Zariski differentials is the bi-dual \(D_ K(R)^{**}\) of the module \(D_ K(R)\) of Kähler differentials. In this paper it is shown that the following conditions are equivalent: (a) \(R\) is quasihomogeneous; (b) The natural homomorphism \(D_ K(R)\otimes K\to D_ K(R)^{**} \otimes K\) is injective, and \(D_ K(R)^{**} \cong A\).
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 13N05
zbMATH DE Number: 572363
zbMATH Keywords: quasihomogeneous isolated singularity
zbMATH Keywords: Auslander-module
zbMATH Keywords: Zariski differentials
reviewed by: Joachim Herzog
MaRDI profile type: Publication
cites work: The Zariski-Lipman conjecture in the graded case
cites work: On two-dimensional quasihomogeneous isolated singularities. I
cites work: Almost Split Sequences and Zariski Differentials
cites work: Derivationen in zweidimensionalen normalen Singularitäten
cites work: Q3995215
full work available at URL: https://doi.org/10.1007/bf01194847
OpenAlex ID: W2099446940
description: scientific article; zbMATH DE number 572363