On the torsion of the differential module of a curve singularity
type: Item
instance of: scholarly article
title: On the torsion of the differential module of a curve singularity
zbMATH Open document ID: 0698.13012
DOI: 10.1007/BF01193622
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: Let R be a complete analytic local k-algebra of dimension one without zero divisors over an algebraically closed field k of characteristic zero. This paper investigates the author's conjecture [cf. Math. Z. 81, 326-354 (1963; Zbl 0113.263)]: R is regular iff \(\Omega_{R/k}\) is torsion-free. In particular the author introduces a ring \(R^*\) between R and \(R_ 1\), the first quadratic transform, and shows that if \(\Omega_{R^*_ k}\) has torsion then R is not regular.
Mathematics Subject Classification ID: 13N05
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 32B05
zbMATH DE Number: 4144111
zbMATH Keywords: differential module
zbMATH Keywords: curve singularity
zbMATH Keywords: complete analytic local algebra
author: Robert W. Berger
reviewed by: Marcel Morales
MaRDI profile type: Publication
cites work: Differentialmoduln eindimensionaler lokaler Ringe
cites work: Cotangent functors of curve singularities
cites work: Q3250654
cites work: Torsion of the differential module of singularities of curves with maximal Hilbert function
description: scientific article; zbMATH DE number 4144111