We prove that a smooth tropical hypersurface in $mathbbR^3$ can be lifted to a smooth embedded Lagrangian submanifold in $(mathbbC^*)^3$. This completes the proof of the result announced in the article "Lagrangian pairs pants" arXiv:1802.02993. The idea of the proof is to use Lagrangian pairs of pants as the main building blocks.
Lagrangian submanifolds from tropical hypersurfaces / D. Matessi. - (2018 Apr 04). [https://doi.org/10.1142/S0129167X21500464]
Lagrangian submanifolds from tropical hypersurfaces
D. Matessi
2018
Abstract
We prove that a smooth tropical hypersurface in $mathbbR^3$ can be lifted to a smooth embedded Lagrangian submanifold in $(mathbbC^*)^3$. This completes the proof of the result announced in the article "Lagrangian pairs pants" arXiv:1802.02993. The idea of the proof is to use Lagrangian pairs of pants as the main building blocks.
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