## Equivalences of families of stacky toric Calabi-Yau hypersurfaces

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- by Charles F. Doran, David Favero and Tyler L. Kelly PDF
- Proc. Amer. Math. Soc.
**146**(2018), 4633-4647 Request permission

## 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.## References

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## Additional Information

**Charles F. Doran**- Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta Canada
- MR Author ID: 643024
- 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
- MR Author ID: 739092
- ORCID: 0000-0002-6376-6789
- 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
- MR Author ID: 874289
- Email: tlk20@dpmms.cam.ac.uk
- 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
- © Copyright 2018 American Mathematical Society
- 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
- MathSciNet review: 3856133