TY - JOUR
T1 - The Special McKay correspondence as an equivalence of derived categories
AU - Craw, Alastair
PY - 2011/9
Y1 - 2011/9
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=80051977332&partnerID=8YFLogxK
UR - http://arxiv.org/abs/0704.3627
UR - http://dx.doi.org/10.1093/qmath/haq006
U2 - 10.1093/qmath/haq006
DO - 10.1093/qmath/haq006
M3 - Article
VL - 62
SP - 573
EP - 591
JO - The Quarterly Journal of Mathematics
JF - The Quarterly Journal of Mathematics
SN - 0033-5606
IS - 3
ER -