A proof of the Popov Conjecture for quivers

Let Q be a quiver with dimension vector α. We show that if the space of isomorphism classes of semisimple representations of Q of dimension vector α is not smooth, then the quotient map is not equidimensional. In other words, we prove the Popov Conjecture for the natural action of the linear reductive group GLα on the space of α-dimensional representations of the quiver Q.