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arXiv · 0803.2990

A derived approach to geometric McKay correspondence in dimension three

Sabin Cautis·Timothy Logvinenko
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Abstract

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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Sabin Cautis, Timothy Logvinenko. 2008-03-20. A derived approach to geometric McKay correspondence in dimension three. https://arxiv.org/abs/0803.2990

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