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November 2020 $G$-constellations and the maximal resolution of a quotient surface singularity
Akira Ishii
Hiroshima Math. J. 50(3): 375-398 (November 2020). DOI: 10.32917/hmj/1607396494

Abstract

For a finite subgroup $G$ of $\mathrm {GL}(2, \mathbb C)$, we consider the moduli space $\mathscr M _\theta$ of $G$-constellations. It depends on the stability parameter $\theta$ and if $\theta$ is generic it is a resolution of singularities of $\mathbb C ^2/G$. In this paper, we show that a resolution $Y$ of $\mathbb C ^2/G$ is isomorphic to $\mathscr M _\theta$ for some generic $\theta$ if and only if $Y$ is dominated by the maximal resolution under the assumption that $G$ is abelian or small.

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Akira Ishii. "$G$-constellations and the maximal resolution of a quotient surface singularity." Hiroshima Math. J. 50 (3) 375 - 398, November 2020. https://doi.org/10.32917/hmj/1607396494

Information

Received: 12 June 2017; Revised: 12 August 2019; Published: November 2020
First available in Project Euclid: 8 December 2020

MathSciNet: MR4184266
Digital Object Identifier: 10.32917/hmj/1607396494

Subjects:
Primary: 14D20
Secondary: 14E16, 14J17

Rights: Copyright © 2020 Hiroshima University, Mathematics Program

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Vol.50 • No. 3 • November 2020
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