Classification of Simple Singularities of Functions

Abstract

By the classification of the singularities belonging to some subset Σ⊂E ^o_n,p of finitely determined map germs f one un-derstands:

• (i) the determination of the normal forms i.e. of some polynomial representatives as simple as possible [e.g. (semi) weighted homogeneous or involving only few monomials] for the equivalence classes Rf or Kf when f ∈ Σ,

• (ii) the description of some partial order (hierarchy) on the set of these equivalence classes which is related to the adjacency of orbits defined in (5.1) and which says roughly which singularity is more complicated than another.