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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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