Enriques diagrams and adjacency of planar curve singularities

We study adjacency of equisingularity types of planar curve singularities in terms of their Enriques diagrams. For linear adjacency a complete answer is obtained, whereas for arbitrary (analytic) adjacency a necessary condition and a sufficient condition are proved. We also show an example of singular curve of type D' that can be deformed to a curve of type D without D' being adjacent to D.