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arXiv · 2209.11900

Moduli of $G$-constellations and crepant resolutions I: the abelian case

Ryo Yamagishi
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Abstract

For a finite abelian subgroup $G\subset SL_n(\mathbb{C})$, we study whether a given crepant resolution $X$ of the quotient variety $\mathbb{C}^n/G$ is obtained as a moduli space of $G$-constellations. In particular we show that, if $X$ admits a natural $G$-constellation family in the sense of Logvinenko over it with all fibers being indecomposable as $\mathbb{C}[\mathbb{C}^n]$-modules, then $X$ is isomorphic to the normalization of a fine moduli space of $G$-constellations.

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Ryo Yamagishi. 2022-09-24. Moduli of $G$-constellations and crepant resolutions I: the abelian case. https://arxiv.org/abs/2209.11900

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