The Special McKay correspondence as an equivalence of derived categories

Details The Special McKay correspondence as an equivalence of derived categories The Special McKay correspondence as an equivalence of derived categories

2007-04-26

arxiv.org/abs/0704.3627v4

Quarterly Journal of Mathematics 62 (2011), 573-591

Mathematics

Algebraic Geometry

17 pages. Final version, to appear in Quart. J. Math

Scientific paper

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).

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