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We propose a three dimensional generalization of the geometric McKaycorrespondence described by Gonzales-Sprinberg and Verdier in dimension two. Wework it out in detail in abelian case. More precisely, we show that theBridgeland-King-Reid derived category equivalence induces a natural geometriccorrespondence between irreducible representations of G and subschemes of theexceptional set of G-Hilb (C^3). This correspondence appears to be related toReid's recipe.

A derived approach to geometric McKay correspondence in dimension three