Bridgeland, T., King, A. and Reid, M. (2001) The McKay correspondence as an equivalence of derived categories. Journal of the American Mathematical Society, 14 (3). pp. 535-554. ISSN 0894-0347
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2001 American Mathematical Society. This is an author produced version of a paper subsequently published in Journal of the American Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 20 Nov 2017 11:02 |
Last Modified: | 20 Nov 2017 11:12 |
Published Version: | http://www.ams.org/journals/jams/2001-14-03/S0894-... |
Status: | Published |
Publisher: | American Mathematical Society |
Refereed: | Yes |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:124062 |