Birational classification of moduli spaces of representations of quivers
Abstract
Let α be a Schur root; let h=hcfv(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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