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The Special McKay correspondence as an equivalence of derived categories

We give a new moduli construction of the minimal resolution of the singularity of type 1/r(1,a) by introducing the Special McKay quiver. To demonstrate that our construction trumps that of the G-Hilbert scheme, we show that the induced tautological line bundles freely generate the bounded derived category of coherent sheaves on X by establishing a suitable derived equivalence. This gives a moduli construction of the Special McKay correspondence for abelian subgroups of GL(2).

preprint2010arXivOpen access
Alastair Craw
math.RTmath.AG
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Alastair Craw

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