Quiver moduli spaces of a given dimension

Abstract: It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined with a combinatorial analysis of dimension vectors in the fundamental set of a wild quiver is applied to prove that in each dimension there are only finitely many projective algebraic varieties occurring as a moduli space of representations of a quiver with a dimension vector that satisfies some simple constraints.