• DOI:10.1090/PROC/13902
• Corpus ID: 39046123

Diagonal splittings of toric varieties and unimodularity

@inproceedings{Chou2016DiagonalSO,
  title={Diagonal splittings of toric varieties and unimodularity},
  author={Jed Chou and Milena Hering and Sam Payne and Rebecca Tramel and Ben Whitney},
  year={2016}
}

• Jed Chou, M. Hering, +2 authors Ben Whitney
• Published 29 December 2016
• Mathematics

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 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.