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arXiv · 2209.11901

Moduli of $G$-constellations and crepant resolutions II: the Craw-Ishii conjecture

Ryo Yamagishi
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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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Ryo Yamagishi. 2022-09-24. Moduli of $G$-constellations and crepant resolutions II: the Craw-Ishii conjecture. https://arxiv.org/abs/2209.11901

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