Article contents
Characterizations of Simple Isolated Line Singularities
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1999
References
- 2
- Cited by