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A derived approach to geometric McKay correspondence in dimension three
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We propose a three dimensional generalization of the geometric McKay correspondence described by Gonzales-Sprinberg and Verdier in dimension two. We work it out in detail when G is abelian and C^3/G has a single isolated singularity. More precisely, we show that the Bridgeland-King-Reid derived category equivalence induces a natural geometric correspondence between irreducible representations of G and subschemes of the exceptional set of G-Hilb (C^3). This correspondence appears to be related to Reid's recipe.
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Walls for $G$-Hilb via Reid's Recipe
The walls of the G-Hilb chamber for finite abelian G in SL3(C) are exactly: Type I walls from (-1,-1)-curves, Type III walls from generalised long sides, and Type 0 walls from exceptional divisors, with all inequaliti...
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