From Tropical Curves to Special Lagrangians
Abstract
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.
Fields of Study & Subjects
Dynamics and Control of Mechanical Systems
Publication details
- Journal / source
- The Quarterly Journal of Mathematics
- Volume
- 77
- Issue
- 3
- Pages
- 735–748
- Publication date
- 30 July 2026
- Language
- EN