Exceptional-curve conjecture for cyclic quotient groups

Let $G$ be a cyclic group of type $\frac{1}{r}(a,b,c)$, and let $\operatorname{EC}(a+b+c)$ denote the collection introduced in the surrounding discussion. The space $G\text{-}\operatorname{Hilb}(\mathbb{C}^{3})$ is the $G$-Hilbert scheme.

Exceptional-curve conjecture. $\operatorname{EC}(a+b+c)$ corresponds to the exceptional curves of $G\text{-}\operatorname{Hilb}(\mathbb{C}^{3})$.

This is proposed as a generalization of the stated results for groups of type $\frac{1}{r}(1,a,r-a)$ and for terminal quotient singularities; its resolution is not indicated in the supplied text.