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

Abstract

Let $W(z_1,\cdots ,z_n):({\mathbb{C}}^{\ast }{)}^n\to \mathbb{C}$ 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.

26 pages, 3 figures. v2: 1. Remove the condition that $0$ needs to be in the interior of the Newton polytope of $W$. 2. Added references and summary of related work in section 0.4. v3. updated grant info

References in corpus (4)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• Mirror symmetry for very affine hypersurfaces
• Arboreal Singularities in Weinstein Skeleta
• Ribbon Graphs and Mirror Symmetry I

Cited by in corpus (5)

• Microlocal Morse theory of wrapped Fukaya categories
• Mirror symmetry for very affine hypersurfaces
• Mirror symmetry for perverse schobers from birational geometry
• Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties
• Gamma II for toric varieties from integrals on T-dual branes and homological mirror symmetry