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arXiv · 2502.16582

Rigidity and Realizability for Tropical Curves in Dimension 3

Jeff Hicks
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Abstract

We present an unobstructedness criterion for Lagrangian threefolds $L\subset X^A$ using the $H_1(L)$-class associated with the boundary of a pseudoholomorphic disk. As an application, let $X^A\to Q$ be a Lagrangian torus fibration whose base $Q$ is a tropical abelian threefold. Given $V\subset Q$ a rigid tropical curve with a pair-of-pants decomposition, we prove that the Lagrangian lift $L_V\subset X^A$ is unobstructed. Provided that an appropriate homological mirror symmetry statement holds, this implies the existence of a realization $Y_V$ in the mirror abelian threefold $X^B\to Q$.

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Jeff Hicks. 2025-02-23. Rigidity and Realizability for Tropical Curves in Dimension 3. https://arxiv.org/abs/2502.16582

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