The Special McKay correspondence as an equivalence of derived categories
Algebraic Geometry
2011-08-25 v4 Representation Theory
Abstract
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).
Keywords
Cite
@article{arxiv.0704.3627,
title = {The Special McKay correspondence as an equivalence of derived categories},
author = {Alastair Craw},
journal= {arXiv preprint arXiv:0704.3627},
year = {2011}
}
Comments
17 pages. Final version, to appear in Quart. J. Math