An upper bound of the singularity order for the generic projection
type: Item
instance of: scholarly article
title: An upper bound of the singularity order for the generic projection
zbMATH Open document ID: 0673.14018
DOI: 10.1016/0022-4049(88)90127-2
author: J. Elias
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let X be an algebroid curve of multiplicity e in \((k^ N,0)\), \(\tilde X\) be Zariski's absolute saturation of X and \(X'\) a generic plane projection of X. The author proves that \(\delta (X')\) is not bigger than \((e-1)\delta(\tilde X)-(e-1)(e-2)/2,\) where \(\delta\) denotes as usual the codimension of the local ring of the singularity in its normalisation. Moreover the author proves that equality holds iff X is isomorphic to the ``monomial curve'' \(t\to (t^ e,t^{e+1},...,t^{2e-1})\).
reviewed by: Alexandru Buium
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14E15
zbMATH DE Number: 4101361
zbMATH Keywords: algebroid curve
zbMATH Keywords: saturation
zbMATH Keywords: generic plane projection
zbMATH Keywords: monomial curve
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90127-2
OpenAlex ID: W2090964769
cites work: Algebroid curves in positive characteristic
cites work: Q3277020
cites work: General Theory of Saturation and of Saturated Local Rings. III. Saturation in Arbitrary Dimension and, in Particular, Saturation of Algebroid Hypersurfaces
cites work: Studies in Equisingularity III: Saturation of Local Rings and Equisingularity
cites work: Q4078152
description: scientific article; zbMATH DE number 4101361