On equivalences of derived and singular categories |
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Authors: | Vladimir Baranovsky Jeremy Pecharich |
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Affiliation: | 1.Mathematics Department,UC-Irvine,Irvine,USA |
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Abstract: | Let X and Y be two smooth Deligne-Mumford stacks and consider a pair of functions f: X → $
mathbb{A}^1
$
mathbb{A}^1
, g:Y → $
mathbb{A}^1
$
mathbb{A}^1
. Assuming that there exists a complex of sheaves on X × $
mathbb{A}^1
$
mathbb{A}^1
Y which induces an equivalence of D b (X) and D b (Y), we show that there is also an equivalence of the singular derived categories of the fibers f −1(0) and g −1(0). We apply this statement in the setting of McKay correspondence, and generalize a theorem of Orlov on the derived category of a Calabi-Yau hypersurface in a weighted projective space, to products of Calabi-Yau hypersurfaces in simplicial toric varieties with nef anticanonical class. |
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Keywords: | |
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