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Equivalences of families of stacky toric Calabi-Yau hypersurfaces


Authors: Charles F. Doran, David Favero and Tyler L. Kelly
Journal: Proc. Amer. Math. Soc. 146 (2018), 4633-4647
MSC (2010): Primary 14M25; Secondary 14C22, 14J33, 14J32, 14J28
DOI: https://doi.org/10.1090/proc/14154
Published electronically: August 10, 2018
MathSciNet review: 3856133
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Abstract | References | Similar Articles | Additional Information

Abstract: Given the same anti-canonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypersurfaces. The applications include: a derived unification of toric mirror constructions, calculations of Picard lattices for linear systems of quartics in $ \mathbf {P}^3$, and a birational reduction of Reid's list to 81 families.


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Additional Information

Charles F. Doran
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta Canada
Email: doran@math.ualberta.ca

David Favero
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta Canada – and – Korea Institute for Advanced Study, Seoul, Republic of Korea
Email: favero@ualberta.ca

Tyler L. Kelly
Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB United Kingdom
Email: tlk20@dpmms.cam.ac.uk

DOI: https://doi.org/10.1090/proc/14154
Keywords: Calabi-Yau varieties, toric varieties, K3 surfaces, derived equivalences, Picard groups, mirror symmetry
Received by editor(s): October 3, 2017
Received by editor(s) in revised form: February 20, 2018, and March 2, 2018
Published electronically: August 10, 2018
Additional Notes: The first author was supported by NSERC, PIMS, and a McCalla professorship at the University of Alberta.
The second author was supported by NSERC through a Discovery Grant and as a Canada Research Chair.
The third author was supported in part by NSF Grant # DMS-1401446 and EPSRC Grant EP/N004922/1.
Communicated by: Lev Borisov
Article copyright: © Copyright 2018 American Mathematical Society