From tropical curves to special Lagrangians

Abstract

We show that any locally planar tropical curve $\Gamma \subset \mathbb{R}^n$ (with unit edge weights) can be realized as the limit of the rescaled moment map images of a family of special Lagrangian submanifolds in $T^*T^n$ with respect to the Euclidean structure. This is based on a gluing construction that matches special Lagrangian local models to the combinatorics of $\Gamma$, thereby establishing a direct link between tropical geometry and special Lagrangian geometry.