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The Special McKay correspondence as an equivalence of derived categories · Around

2007

The Special McKay correspondence as an equivalence of derived categories

Craw, Alastair

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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).

Built on

Deformationen von Quotientensingularitäten (nach zyklischen Gruppen)
O. Riemenschneider · 1974
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Reflexive modules on cyclic quotient surface singularities
J. Wunram · 1987
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Reflexive modules on quotient surface singularities
J. Wunram · 1988
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Moduli of representations of finite-dimensional algebras
A. King · 1994
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The homogeneous coordinate ring of a toric variety
D. Cox · 1995
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