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

2024/05/15 by Capellan, John Ashley Navarro
#14D20 #14E16 #14J17 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2405.09491

Abstract

A conjecture in [Ish20] states that for a finite subgroup G of GL(2; ℂ), a resolution Y of ℂ²/G is isomorphic to a moduli space M_θ of G-constellations for some generic stability parameter θ 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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