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Characterizations of Simple Isolated Line Singularities

Published online by Cambridge University Press:  20 November 2018

Alexandru Zaharia
Alexandru Zaharia*
Affiliation:
Institute of Mathematics, of The Romanian Academy
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Abstract

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A line singularity is a function germ $f:\,\left( {{\text{C}}^{n+1}},\,0 \right)\,\to \,\text{C}$ with a smooth 1-dimensional critical set $\sum \,=\,\left\{ \left( x,\,y \right)\,\in \,\text{C}\,\times \,{{\text{C}}^{n}}\,|\,y\,=\,0 \right\}$. An isolated line singularity is defined by the condition that for every $x\,\ne \,0$, the germ of $f$ at $\left( x,\,0 \right)$ is equivalent to $y_{1}^{2}\,+\,\cdot \,\cdot \,\cdot \,+\,y_{n}^{2}$. Simple isolated line singularities were classified by Dirk Siersma and are analogous of the famous $A\,-\,D\,-E$ singularities. We give two new characterizations of simple isolated line singularities.

Keywords

32S2514B05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 4 , 01 December 1999 , pp. 499 - 506
Copyright
Copyright © Canadian Mathematical Society 1999

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