Characterizations of Simple Isolated Line Singularities

Zaharia, Alexandru

Canadian mathematical bulletin, Tome 42 (1999) no. 4, pp. 499-506

Résumé

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.

Détail

DOI : 10.4153/CMB-1999-057-2

Mots-clés : 32S25, 14B05