Irreducibility of the moduli space for the quotient singularity $\frac{1}{2k+1}(k+1,1,2k)$
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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 $\mth$ of $\theta$-stable $G$-constellations for a suitable $\theta$. This paper proves that each connected component of the moduli space $\mth$ has a torus fixed point and classifies all torus fixed points on $\mth$. By product, we show that for $\frac{1}{2k+1}(k+1,1,-1)$ case the moduli space $\mth$ is irreducible.
Abstract
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 $\mth$ of $\theta$-stable $G$-constellations for a suitable $\theta$. This paper proves that each connected component of the moduli space $\mth$ has a torus fixed point and classifies all torus fixed points on $\mth$. By product, we show that for $\frac{1}{2k+1}(k+1,1,-1)$ case the moduli space $\mth$ is irreducible.
참고문헌 (10)
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