How to Draw Tropical Planes

TL;DR

This paper explores the parameter spaces of tropical planes, explicitly computing them for small cases, and uses combinatorial representations like matroid subdivisions and tree arrangements to visualize these tropical objects.

Contribution

It provides explicit computations of the Dressian and tropical Grassmannian for n ≤ 7 and links these to combinatorial models for visualization.

Findings

Explicit descriptions of tropical Grassmannian and Dressian for n ≤ 7

Connections between tropical planes, matroid subdivisions, and tree arrangements

Visual representations of tropical planes using combinatorial models

Abstract

The tropical Grassmannian parameterizes tropicalizations of linear spaces, while the Dressian parameterizes all planes in $\TP^{n-1}$. We study these parameter spaces and we compute them explicitly for $n \leq 7$. Planes are identified with matroid subdivisions and with arrangements of trees. These representations are used to draw pictures.