MINIMAL SINGULARITIES FOR REPRESENTATIONS OF DYNKIN QUIVERS

We develop some reduction techniques for the study of singularities in orbit closures of finite dimensional modules. This enables us to clas sify all singularities occurring in minimal degenerations of represent ations of Dynkin quivers. They are all smoothly equivalent to the sing ularity at the zero-matrix inside the p x q-matrices of rank at most o ne.