Bull. Korean Math. Soc. 2024; 61(2): 519-527
Online first article August 30, 2023 Printed March 31, 2024
https://doi.org/10.4134/BKMS.b230215
Copyright © The Korean Mathematical Society.
Seung-Jo Jung
Jeonbuk National University
For a finite subgroup $G$ of $GL_n(\mathbb C)$, the moduli space $\mathcal M_{\theta}$ of $\theta$-stable $G$-constellations is rarely smooth. This note shows that for a group $G$ of type $\frac{1}{r}(1,a,b)$ with $r=abc+a+b$, there is a generic stability parameter $\theta\in \Theta$ such that the birational component $Y_{\theta}$ of $\theta$-stable $G$-constellations provides a resolution of the quotient singularity $X:=\mathbb C^3/G$.
Keywords: $G$-constellations, quotient singularities
MSC numbers: 14B05, 14J17
Supported by: This work was partially supported by NRF grant (NRF-2021R1C1C1004097) of the Korean government.
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd