# Lagrangian skeleta of hypersurfaces in $$({\mathbb {C}}^*)^n$$

@article{Zhou2018LagrangianSO,
title={Lagrangian skeleta of hypersurfaces in \$\$(\{\mathbb \{C\}\}^*)^n\$\$},
author={Peng Zhou},
journal={arXiv: Symplectic Geometry},
year={2018}
}
• Peng Zhou
• Published 1 March 2018
• Mathematics
• arXiv: Symplectic Geometry
Let $W(z_1, \cdots, z_n): (\mathbb{C}^*)^n \to \mathbb{C}$ be a Laurent polynomial in $n$ variables, and let $\mathcal{H}$ be a generic smooth fiber of $W$. In \cite{RSTZ} Ruddat-Sibilla-Treumann-Zaslow give a combinatorial recipe for a skeleton for $\mathcal{H}$. In this paper, we show that for a suitable exact symplectic structure on $\mathcal{H}$, the RSTZ-skeleton can be realized as the Liouville Lagrangian skeleton.
8 Citations

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