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Moduli of $G$-constellations and crepant resolutions II: the Craw-Ishii conjecture (2209.11901v3)

Published 24 Sep 2022 in math.AG

Abstract: For any given finite subgroup $G\subset SL_3(\mathbb{C})$, we show that every projective crepant resolution $X$ of the quotient variety $\mathbb{C}3/G$ is isomorphic to the moduli space of $\theta$-stable $G$-constellations for a generic stability condition $\theta$, as conjectured by Craw and Ishii. We also show that generators of the Cox ring of $X$ can be obtained from semi-invariants for representations of the McKay quiver of $G$.

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