Lagrangian Skeleta of Hypersurfaces in $(\mathbb{C}^*)^n$

Peng Zhou

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Lagrangian Skeleta of Hypersurfaces in (mathbb{C}^*)^n

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arxiv 1803.00320 v3 pith:SDH743NS submitted 2018-03-01 math.SG

Lagrangian Skeleta of Hypersurfaces in (mathbb{C}^*)^n

Peng Zhou This is my paper

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keywords mathbbmathcallagrangianskeletoncdotscitecombinatorialexact

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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.

Lagrangian Skeleta of Hypersurfaces in (mathbb{C}^*)^n

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