Local geometry of smooth curves passing through rational double points
type: Item
instance of: scholarly article
title: Local geometry of smooth curves passing through rational double points
zbMATH Open document ID: 0757.14020
DOI: 10.1007/BF01934346
author: David B. Jaffe
published in: Mathematische Annalen
publication date: 1993-01-12T00:00:00Z
full work available at URL: https://eudml.org/doc/165022
review text: We study the local geometry of smooth curves on singular surfaces. This amounts to the following problem in local algebra: Classify pairs \((R,p)\) consisting of a complete local \(\mathbb{C}\)-algebra \(R\), together with a height one prime ideal \(p\) of \(R\) such that \(R/p\) is regular. It is assumed that \(R\) is the complete local ring of a singular point on a variety. Two pairs \((R,p)\) and \((R',p')\) are isomorphic if there exists an isomorphism of \(\mathbb{C}\)-algebras from \(R\) to \(R'\) which carries \(p\) to \(p'\). A complete solution is given in the special case where \(R\) corresponds to a rational double point.
Mathematics Subject Classification ID: 14H99
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14F45
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 86218
zbMATH Keywords: local geometry of smooth curves on singular surfaces
zbMATH Keywords: rational double point
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 86218