Lagrangian submanifolds from tropical hypersurfaces

Abstract

We prove that a smooth tropical hypersurface in ${\mathbb{R}}^3$ can be lifted to a smooth embedded Lagrangian submanifold in $({\mathbb{C}}^{\ast }{)}^3$. 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.

59 pages, 14 Figures. This article completes the proof of the result announced in "Lagrangian pairs pants" arXiv:1802.02993

References in corpus (5)

• Lagrangian pairs of pants
• Tropical Lagrangian Hypersurfaces are Unobstructed
• Tropically constructed Lagrangians in mirror quintic threefolds
• Tropical Lagrangians in toric del-Pezzo surfaces
• Lagrangian 3-torus fibrations

Cited by in corpus (5)

• Lagrangian pairs of pants
• Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves
• Tropically constructed Lagrangians in mirror quintic threefolds
• Spherical twists and Lagrangian spherical manifolds
• The Gamma Conjecture for Tropical Curves in Local Mirror Symmetry