Adjoint action of automorphism groups on radical endomorphisms, generic equivalence and Dynkin quivers

Let Q be a connected quiver with no oriented cycles, k the field of complex numbers and P a projective representation of Q. We study the adjoint action of the automorphism group Aut_kQ P on the space of radical endomorphisms radEnd_kQ P. Using generic equivalence, we show that the quiver Q has the property that there exists a dense open Aut _kQ P-orbit in radEnd_kQ P, for all projective representations P, if and only if Q is a Dynkin quiver. This gives a new characterisation of Dynkin quivers.