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Derived McKay correspondence via pure-sheaf transforms
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Logvinenko, Timothy (2008) Derived McKay correspondence via pure-sheaf transforms. Mathematische Annalen, Vol.341 (No.1). pp. 137-167. doi:10.1007/s00208-007-0186-z ISSN 0025-5831.
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Official URL: http://dx.doi.org/10.1007/s00208-007-0186-z
Abstract
In most cases where it has been shown to exist the derived McKay correspondence D(Y)−→∼DG(Cn) can be written as a Fourier–Mukai transform which sends point sheaves of the crepant resolution Y to pure sheaves in DG(Cn) . We give a sufficient condition for E∈DG(Y×Cn) to be the defining object of such a transform. We use it to construct the first example of the derived McKay correspondence for a non-projective crepant resolution of C3/G . Along the way we extract more geometrical meaning out of the Intersection Theorem and learn to compute θ-stable families of G-constellations and their direct transforms.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Mathematische Annalen | ||||
Publisher: | Springer Verlag | ||||
ISSN: | 0025-5831 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.341 | ||||
Number: | No.1 | ||||
Page Range: | pp. 137-167 | ||||
DOI: | 10.1007/s00208-007-0186-z | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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