Diagonal splittings of toric varieties and unimodularity
Algebraic Geometry
2025-01-07 v2 Combinatorics
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 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.
Cite
@article{arxiv.1612.09208,
title = {Diagonal splittings of toric varieties and unimodularity},
author = {Jed Chou and Milena Hering and Sam Payne and Rebecca Tramel and Ben Whitney},
journal= {arXiv preprint arXiv:1612.09208},
year = {2025}
}
Comments
11 pages v2: minor revisions, to appear in Proc. Amer. Math. Soc