On minimal disjoint degenerations of modules over tame path algebras

For representations of tame quivers the degenerations are controlled by the dimensions of various homomorphism spaces. Furthermore, there is no proper degeneration to an indecomposable. Therefore, up to common direct summands, any minimal degeneration from M to N is induced by a short exact sequence 0→U→M→V→0 with indecomposable ends that add up to N. We study these ‘building blocs’ of degenerations and we prove that the codimensions are bounded by two. Therefore, a quiver is Dynkin resp. Euclidean resp. wild iff the codimension of the building blocs is one resp. bounded by two resp. unbounded. We explain also that for tame quivers the complete classification of all the building blocs is a finite problem that can be solved with the help of a computer.