Toric flat families, valuations, and tropical geometry over the semifield of piecewise linear functions
Kiumars Kaveh, Christopher Manon · arXiv (Cornell University) · 2019
Using the notion of a valuation into the semifield of piecewise linear functions, we give a classification of torus equivariant flat families of finite type over a toric variety base, by certain piecewise linear maps between fans. As a consequence we derive a classification of toric vector bundles phrased in terms of tropicalized linear spaces. We use these tools to give a characterization of the Mori dream space property for a projectivized toric vector bundle.