# 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}
}
• 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…
2 Citations
. Let J be any ideal in a strongly F -regular, diagonally F -split ring R essentially of ﬁnite type over an F -ﬁnite ﬁeld. We show that J s ` t Ď τ p J s ´ ε q τ p J t ´ ε q for all s,t,ε ą 0 for

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