Bulletin of the
Korean Mathematical Society BKMS

A 3-fold quotient terminal singularity is of the type $\frac{1}{r}(b,1$, $-1)$ with $\gcd(r,b)=1$. In \cite{Terminal}, it is proved that the economic resolution of a 3-fold terminal quotient singularity is isomorphic to a distinguished component of a moduli space $\mathcal M_{\theta}$ of $\theta$-stable $G$-constellations for a suitable $\theta$. This paper proves that each connected component of the moduli space $\\mathcal M_{\theta}$ has a torus fixed point and classifies all torus fixed points on $\mathcal M_{\theta}$. By product, we show that for $\frac{1}{2k+1}(k+1,1,-1)$ case the moduli space $\mathcal M_{\theta}$ is irreducible.

Keywords: Terminal quotient singularities, economic resolutions

MSC numbers: 14B05,14J17

Supported by: This work was partially supported by NRF grant (NRF-2021R1C1C1004097) of the Korean government.