Tropical Lagrangian Hypersurfaces are Unobstructed

We produce for each tropical hypersurface $V(ϕ)\subset Q=\mathbb{R}^n$ a Lagrangian $L(ϕ)\subset (\mathbb{C}^*)^n$ whose moment map projection is a tropical amoeba of $V(ϕ)$. When these Lagrangians are admissible in the Fukaya-Seidel category, we show that they are unobstructed objects of the Fukaya category, and mirror to sheaves supported on complex hypersurfaces in a toric mirror.

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