Abstract
Let α be a Schur root; let h = hcf v (α( v)) and let p = 1 − 〈α/ h, α/ h〉. Then a moduli space of representations of dimension vector α is birational to p h by h matrices up to simultaneous conjugacy. Therefore, if h = 1, 2, 3 or 4, then such a moduli space is a rational variety and if h divides 420 it is a stably rational variety.
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