Proof of a conjecture of Batyrev and Nill
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Abstract
We prove equivalences of derived categories for the various mirrors in the Batyrev-Borisov construction. In particular, we obtain a positive answer to a conjecture of Batyrev and Nill. The proof involves passing to an associated category of singularities and toric variation of geometric invariant theory quotients.
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American Journal of Mathematics
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0002-9327
1080-6377
1080-6377
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Johns Hopkins University Press
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Engineering and Physical Sciences Research Council (EP/N004922/1)
The second-named author thanks the Pacific Institute for the Mathematical Sciences and NSERC for various forms of support. Frequent visits to the University of Alberta greatly expedited the progress of this work. The first-named author is also indebted to the NSERC for support provided by a Canada Research Chair and Discovery Grant. The second-named author acknowledges that this material is based upon work supported by the National Science Foundation under Award No. DMS-1401446 and the Engineering and Physical Sciences Research Council under Grant EP/N004922/1.