I 've heard that a quiver representation $R_{Q}$ of a quiver $Q$ is a variety (I guess they mean an algebraic variety). Is this is the case we know that an algebraic variety is given by the zero set of a collection of polynomials. In the case of quivers what is this zero set that makes them form an algebraic variety?
Furthermore in every node (vector space) we assign the natural action of the endomorphisms. If we quotient out the representation by this action we obtain a stack. $$ R_Q / \prod_i G_{\text{dim}V_i}(Vi) $$ Here $V_i$ denotes the vector space that lives in the $i$-th node of $Q$. Is this the usual algebraic stack we talk about in algebraic geometry? Can I think of it as an orbifold with some singular points? And what these points would be?