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arXiv · 2405.09491

The McKay Correspondence for Dihedral Groups: The Moduli Space and the Tautological Bundles

John Ashley Navarro Capellan
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Abstract

A conjecture in [Ish20] states that for a finite subgroup $G$ of $GL(2; \mathbb{C})$, a resolution $Y$ of $\mathbb{C}^2/G$ is isomorphic to a moduli space $\mathcal{M}_{\theta}$ 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 (via [IN1], [IN2], and [Ish02]). To appear in Hiroshima Mathematical Journal.

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John Ashley Navarro Capellan. 2024-05-15. The McKay Correspondence for Dihedral Groups: The Moduli Space and the Tautological Bundles. https://arxiv.org/abs/2405.09491

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