## Diagonal splittings of toric varieties and unimodularity

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- by Jed Chou, Milena Hering, Sam Payne, Rebecca Tramel and Ben Whitney PDF
- Proc. Amer. Math. Soc.
**146**(2018), 1911-1920 Request permission

## Abstract:

We use a polyhedral criterion for the existence of diagonal splittings to investigate which toric varieties $X$ are diagonally split. Our results are stated in terms of the vector configuration given by primitive generators of the 1-dimensional cones in the fan defining $X$. We show, in particular, that $X$ is diagonally split at all $q$ if and only if this configuration is unimodular, and that $X$ is not diagonally split at any $q$ if this configuration is not $2$-regular. We also study implications for the possibilities for the set of $q$ at which a toric variety $X$ is diagonally split.## References

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## Additional Information

**Jed Chou**- Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
- Email: jedchou1@illinois.edu
**Milena Hering**- Affiliation: School of Mathematics, University of Edinburgh, Edinburgh, EH9 3JZ, United Kingdom
- MR Author ID: 722657
- Email: m.hering@ed.ac.uk
**Sam Payne**- Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06511
- MR Author ID: 652681
- Email: sam.payne@yale.edu
**Rebecca Tramel**- Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
- Email: rtramel@illinois.edu
**Ben Whitney**- Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
- Email: ben_whitney@brown.edu
- Received by editor(s): January 6, 2017
- Received by editor(s) in revised form: July 4, 2017
- Published electronically: December 7, 2017
- Additional Notes: Portions of this research were carried out during an REU project supported under NSF grant DMS-1001859.

The work of the second author was partially supported by EPSRC first grant EP/K041002/1.

The work of the third author was partially supported by NSF CAREER DMS-1149054. - Communicated by: Lev Borisov
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**146**(2018), 1911-1920 - MSC (2010): Primary 14M25, 52B20; Secondary 13A35, 90C10
- DOI: https://doi.org/10.1090/proc/13902
- MathSciNet review: 3767345