Kavli Affiliate: Yukari Ito
| Summary:
In this paper, we investigate the relations among various results concerning the minimal resolution of cyclic quotient singularities of the form $mathbbC^2/G$. We refer to these as "bamboo-type" singularities, since the dual graphs of the exceptional curves in their resolutions resemble the shape of bamboo. We present classical results on the minimal resolution of singularities, the $G$-Hilbert scheme, the generalized McKay correspondence, deformations of singularities, and quiver varieties. These results have been obtained independently in different contexts, and here we provide a unified exposition enriched with numerous examples, which we hope will serve as a useful guide to the study of two-dimensional cyclic singularities. Moreover, this survey aims to offer insights that may inspire generalizations to non-cyclic singularities and to higher-dimensional quotient singularities.
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