Simple singularities of curves

V.I.Arnold

A singularity of a curve below means a germ of a holomorphic mapping of 
the complex line into the complex space at a singular point (where the
derivative of the mapping vanishes) considered up to the biholomorphic
mappings of the image space.

The singularity is called simple if all neighbouring singularities belong 
to a finite set of equivalence classes (have no moduli). The simple
singularities of curves in the plane have been classified by J.W.Bruce and
T.Gaffney, that of curves in three-space -- by C.Gibson and C.Hobbs.

The singularity is called stably simple if it is simple and remains simple
when the ambient space is embedded into a larger space. Two curves, obtained
one from the other by such an embedding, are called stably equivalent.

We classify below the simple curve singularities in spaces of any dimension
up to stable equivalence.