Representations of quivers with free module of covariants

Given a finite quiver Q of Dynkin type An, it is well known that the ring of semi-invariants SI(Q,d) is a polynomial ring. We show that the ideal defined by semi-invariants of positive degree in Rep(Q,d) is a complete intersection. It follows that the action of SL(Q,d) on Rep(Q,d) gives a cofree representation. In particular, we have that the modules of covariants are free k[Rep(Q,d)]SL(Q,d)-modules.