Codimension two singularities for representations of extended Dynkin quivers

Let M and N be two representations of an extended Dynkin quiver such that the orbit O_N of N is contained in the orbit closure \bar{O_M} and has codimension two. We show that the pointed variety $(\overline{O_M},N)$ is smoothly equivalent to a simple surface singularity of type A_n, or to the cone over a rational normal curve.