THE SPECIAL McKAY CORRESPONDENCE AS AN EQUIVALENCE OF DERIVED CATEGORIES
Alastair Craw · The Quarterly Journal of Mathematics · 2010
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).