From tropical curves to special Lagrangians
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915480311169024 |
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| author | Chiu, Shih-Kai Li, Yang Lin, Yu-Shen |
| author_facet | Chiu, Shih-Kai Li, Yang Lin, Yu-Shen |
| contents | We show that any locally planar tropical curve $Γ\subset \mathbb{R}^n$ (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 $Γ$, thereby establishing a direct link between tropical geometry and special Lagrangian geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04843 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From tropical curves to special Lagrangians Chiu, Shih-Kai Li, Yang Lin, Yu-Shen Differential Geometry We show that any locally planar tropical curve $Γ\subset \mathbb{R}^n$ (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 $Γ$, thereby establishing a direct link between tropical geometry and special Lagrangian geometry. |
| title | From tropical curves to special Lagrangians |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.04843 |