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On the Canonical Ideals of One-Dimensional Cohen–Macaulay Local Rings

Part of: Local rings and semilocal rings Local theory

Published online by Cambridge University Press:  13 July 2015

Juan Elias
Juan Elias*
Affiliation:
Departament d'Àlgebra i Geometria, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain (elias@ub.edu)
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Abstract

In this paper we consider the problem of explicitly finding canonical ideals of one-dimensional Cohen–Macaulay local rings. We show that Gorenstein ideals contained in a high power of the maximal ideal are canonical ideals. In the codimension 2 case, from a Hilbert–Burch resolution, we show how to construct canonical ideals of curve singularities. Finally, we translate the problem of the analytic classification of curve singularities to the classification of local Artin Gorenstein rings with suitable length.

Keywords

canonical idealGorensteinCohen–MacaulayHilbert–Samuel function

MSC classification

Secondary: 14B05: Singularities 13H15: Multiplicity theory and related topics 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 77 - 90
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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