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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.04472 |
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Table of Contents:
- In this paper, we investigate the relations among various results concerning the minimal resolution of cyclic quotient singularities of the form $\mathbb{C}^2/G$. 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.