SINGULAR Examples

Space Curve Singularities

The ideal of a space curve singularity X is generated by the maximal minors of its presentation matrix M:

Any deformation of X is given by a perturbation of M.

where

with g denoting the map

$\displaystyle \Mat (k+1, k+1, \mathbb{C}[[\underline{x}]]) \times \Mat (k , k, \mathbb{C}[[\underline{x}]])$	$\displaystyle \stackrel{g}{\longrightarrow}$	$\displaystyle \Mat (k, k+1, \mathbb{C}[[\underline{x}]])\,,$
$\displaystyle (A,B)$	$\displaystyle \longmapsto$	$\displaystyle AM + MB \,.$

Lille, 08-07-02