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arXiv · 1709.00366

Incidence geometry and universality in the tropical plane

Milo Brandt·Michelle Jones·Catherine Lee·Dhruv Ranganathan
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Abstract

We examine the incidence geometry of lines in the tropical plane. We prove tropical analogs of the Sylvester-Gallai and Motzkin-Rabin theorems in classical incidence geometry. This study leads naturally to a discussion of the realizability of incidence data of tropical lines. Drawing inspiration from the von Staudt constructions and Mnëv's universality theorem, we prove that determining whether a given tropical linear incidence datum is realizable by a tropical line arrangement requires solving an arbitrary linear programming problem over the integers.

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Milo Brandt, Michelle Jones, Catherine Lee, Dhruv Ranganathan. 2018-05-13. Incidence geometry and universality in the tropical plane. https://arxiv.org/abs/1709.00366

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