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Birational classification of moduli spaces of representations of quivers

Aidan Schofield
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Abstract

Let αbe 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 αis 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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Aidan Schofield. 1999-11-02. Birational classification of moduli spaces of representations of quivers. https://arxiv.org/abs/math/9911014

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