Resolution of quotient singularities via $G$-constellations
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For a finite subgroup $G$ of $\GL_n(\C)$, the moduli space $\mth$ 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 $\yth$ of $\theta$-stable $G$-constellations provides a resolution of the quotient singularity $X:=\C^3/G$.
Abstract
For a finite subgroup $G$ of $\GL_n(\C)$, the moduli space $\mth$ 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 $\yth$ of $\theta$-stable $G$-constellations provides a resolution of the quotient singularity $X:=\C^3/G$.
참고문헌 (9)
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