Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
| dc.creator | Bridgeland, Tom | |
| dc.creator | King, Alastair | |
| dc.creator | Reid, Miles | |
| dc.date | 1999-08-06 | |
| dc.date | 2000-05-02 | |
| dc.date.accessioned | 2026-07-07T05:30:12Z | |
| dc.date.available | 2026-07-07T05:30:12Z | |
| dc.description | Let G be a finite group of automorphisms of a nonsingular complex threefold M such that the canonical bundle omega_M is locally trivial as a G-sheaf. We prove that the Hilbert scheme Y=GHilb M parametrising G-clusters in M is a crepant resolution of X=M/G and that there is a derived equivalence (Fourier- Mukai transform) between coherent sheaves on Y and coherent G-sheaves on M. This identifies the K theory of Y with the equivariant K theory of M, and thus generalises the classical McKay correspondence. Some higher dimensional extensions are possible. | |
| dc.description | Dedicated to Andrei Tyurin's 60th birthday. This draft is completely rewritten; it contains in particular a complete proof of Nakamura's conjecture that the Hilbert scheme of G-clusters is a crepant resolution for G in SL(3,C). 27 pp. submitted to J. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/9908027 | |
| dc.identifier | http://arxiv.org/abs/math/9908027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78921 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Mukai implies McKay: the McKay correspondence as an equivalence of derived categories | |
| dc.type | text |