Resolution
Global GMS
ES Strata
Build. Blocks
Comb. Appl.
HCA Proving
Arrangements
Branches
Classify
Coding
Deformations
Equidim Part
Existence
Finite Groups
Flatness
Genus
Hilbert Series
Membership
Nonnormal Locus
Normalization
Primdec
Puiseux
Plane Curves
Saturation
Solving
Space Curves
Spectrum
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
$\displaystyle \Mat (k+1, k+1, \mathbb{C}[[\underline{x}]]) imes \Mat (k , k, \mathbb{C}[[\underline{x}]])$ $\displaystyle \stackrel{g}{\longrightarrow}$ $\displaystyle \Mat (k, k+1, \mathbb{C}[[\underline{x}]])\,,$  
$\displaystyle (A,B)$ $\displaystyle \longmapsto$ $\displaystyle AM + MB \,.$  


Stratification - An Example
KL, 06/03 http://www.singular.uni-kl.de