Bulletin of the
Korean Mathematical Society BKMS

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.