VOL. 88 | 2023 Moduli of $G$-constellations and crepant resolutions I: the abelian case
Ryo Yamagishi

Editor(s) Yukari Ito, Akira Ishii, Osamu Iyama

Adv. Stud. Pure Math., 2023: 159-193 (2023) DOI: 10.2969/aspm/08810159

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.

Information

Published: 1 January 2023
First available in Project Euclid: 8 May 2023

Digital Object Identifier: 10.2969/aspm/08810159

Subjects:
Primary: 14E16
Secondary: 14M25 , 16G20

Keywords: McKay correspondence , quiver representations , toric geometry

Rights: Copyright © 2023 Mathematical Society of Japan

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