2000 character limit reached
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 $G$.