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

A conjecture in [Ish20] states that for a finite subgroup $G$ of $GL(2;\mathbb{C})$, a resolution $Y$ of ${\mathbb{C}}^2\mathrm{/}G$ 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.