Birational classification of moduli spaces of representations of quivers

Mathematics – Algebraic Geometry

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Scientific paper

Let \alpha be a Schur root; let h=hcf_v(\alpha(v)) and let p = 1 - <
\alpha/h,\alpha/h >. Then a moduli space of representations of dimension vector
\alpha 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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