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arXiv · 1612.09208

Diagonal splittings of toric varieties and unimodularity

Jed Chou·Milena Hering·Sam Payne·Rebecca Tramel·Ben Whitney
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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.

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Jed Chou, Milena Hering, Sam Payne, Rebecca Tramel, Ben Whitney. 2016-12-29. Diagonal splittings of toric varieties and unimodularity. https://arxiv.org/abs/1612.09208

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