On two-dimensional quasihomogeneous isolated singularities. I
type: Item
instance of: scholarly article
title: On two-dimensional quasihomogeneous isolated singularities. I
zbMATH Open document ID: 0792.14003
DOI: 10.1007/BF01194846
author: Alex Martsinkovsky
published in: Archiv der Mathematik
publication date: 1994-06-30T00:00:00Z
review text: In the mid-eighties the author conjectured that a two-dimensional integrally closed analytic \(k\)-algebra over an algebraically closed field \(k\) of characteristic 0 is graded if and only if the module of Zariski differentials is isomorphic to the Auslander module. (The latter can be defined as the (minimal) Cohen-Macaulay approximation of the maximal ideal.) In the present paper the ``if'' part of the conjecture is proved for hypersurface rings. The ``only if'' part is shown to be always true.
reviewed by: Alex Martsinkovsky
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 13J07
Mathematics Subject Classification ID: 14J70
zbMATH DE Number: 572362
zbMATH Keywords: gradation of analytic algebra
zbMATH Keywords: integrally closed domain
zbMATH Keywords: Zariski differentials
zbMATH Keywords: Auslander module
zbMATH Keywords: hypersurface rings
MaRDI profile type: Publication
cites work: Rational Singularities and Almost Split Sequences
cites work: Stable module theory
cites work: On Auslander modules of normal surface singularities
cites work: Homological Algebra on a Complete Intersection, with an Application to Group Representations
cites work: Q5202294
cites work: Almost Split Sequences and Zariski Differentials
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cites work: The Poincaré series of a local ring
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description: scientific article; zbMATH DE number 572362