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On adjunctions for Fourier–Mukai transforms
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Anno, Rina and Logvinenko, Timothy (2012) On adjunctions for Fourier–Mukai transforms. Advances in Mathematics, Vol.231 (No.3-4). pp. 2069-2115. doi:10.1016/j.aim.2012.06.007 ISSN 0001-8708.
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Official URL: http://dx.doi.org/10.1016/j.aim.2012.06.007
Abstract
We show that the adjunction counits of a Fourier-Mukai transform Phi: D(X-1) -> D(X-2) arise from maps of the kernels of the corresponding Fourier-Mukai transforms. In a very general setting of proper separable schemes of finite type over a field we write down these maps of kernels explicitly - facilitating the computation of the twist (the cone of an adjunction counit) of Phi. We also give another description of these maps, better suited to computing cones if the kernel of Phi is a pushforward from a closed subscheme Z C X-1 X-2. Moreover, we show that we can replace the condition of properness of the ambient spaces X-1 and X-2 by that of Z being proper over them and still have this description apply as is. This can be used, for instance, to compute spherical twists on non-proper varieties directly and in full generality. (C) 2012 Elsevier Inc. All rights reserved.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Advances in Mathematics | ||||
Publisher: | Academic Press | ||||
ISSN: | 0001-8708 | ||||
Official Date: | October 2012 | ||||
Dates: |
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Volume: | Vol.231 | ||||
Number: | No.3-4 | ||||
Page Range: | pp. 2069-2115 | ||||
DOI: | 10.1016/j.aim.2012.06.007 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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