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The McKay Correspondence for Dihedral Groups: The Moduli Space and the Tautological Bundles (2405.09491v3)
Published 15 May 2024 in math.AG and math.RT
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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