A proof of the Popov Conjecture for quivers

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