Abstract
Let R be the local ring of a reduced plane curve singularity. It is shown that R is the ring of a strictly unimodular singularity if and only if it admits finitely many at most 1-parameter families of isomorphism classes of torsion free rank 1 modules.
Keywords
- Local Ring
- Isomorphism Class
- Plane Curve
- Curve Singularity
- Principal Ideal Ring
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References
V.I. ARNOL’D: Critical Points of Smooth Functions and their Normal Forms. RMS 30:5 (1975), 1–75
R.-O. BUCHWEITZ, G.-M. GREUEL, F.-O. SCHREYER: Cohen-Macaulay-Modules on Hypersurface Singularities, Part II; Invent. math. 88, pp 165–182, 1987
E. DIETERICH: Classification of the Indecomposable Representations of the Cyclic Group of Order Three in a Complete Discrete Valuation Ring of Ramification Degree Four. Preprint Universität Bielefeld, 1985.
G.-M. GREUEL, H. KNÖRRER: Einfache Kurvensingularitäten und torsionsfreie Moduln; Math. Ann. 270 (1985), 417–425
C. KAHN: Reflexive Moduln auf einfach elliptischen Flächensingularitäten; Preprint Max Planck Institut für Mathematik, Bonn 1987
H. KNÖRRER: Cohen-Macaulay-Modules on Hypersurface Singularities, Part I; Invent. math. 88, pp. 153–164, 1987
H. KNÖRRER: Torsionsfreie Moduln bei Deformation von Kurvensingularitäten; these Proceedings
F.-O. SCHREYER: Finite and Countable CM-Representation Type; these Proceedings
A. SCHAPPERT: Die Klassifikation aller torsionsfreier Moduln vom Rang 1 über den unimodularen Kurvensingularitäten; Diplomarbeit, Kaiserslautern 1985
C.T.C. WALL: Classification of Unimodal Isolated Singularities of Complete Intersections; Proceedings of Symp. in Pure Mathematics, 40 (1983), 625–640
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© 1987 Springer-Verlag
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Schappert, A. (1987). A characterisation of strictly unimodular plane curve singularities. In: Greuel, GM., Trautmann, G. (eds) Singularities, Representation of Algebras, and Vector Bundles. Lecture Notes in Mathematics, vol 1273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078843
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DOI: https://doi.org/10.1007/BFb0078843
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-540-47851-5
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