The McKay correspondence for dihedral groups: The moduli space and the tautological bundles
Abstract
A conjecture posed by Ishii states that for a finite subgroup $G$ of $\mathrm{GL}(2, \mathbb C)$, a resolution $Y$ of $\mathbb C^2/G$ is isomorphic to a moduli space $\mathscr M_\theta$ of $G$-constellations for some generic stability parameter $\theta$ if and only if $Y$ is dominated by the maximal resolution. This paper affirms the conjecture in the case of dihedral groups as a class of complex reflection groups, and offers an extension of McKay correspondence of Ito-Nakamura for $\mathrm{SL}(2, \mathbb C)$, and Ishii for small $\mathrm{GL}(2, \mathbb C)$.
Fields of Study & Subjects
Mathematics and Applications
Advanced Algebra and Geometry
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Hiroshima Mathematical Journal
- Volume
- 56
- Issue
- 1
- Pages
- 131–131
- Publication date
- 1 March 2026
- Language
- EN