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.
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