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

Peng Zhou

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

Symplectic Geometry 2018-10-31 v3

Authors: Peng Zhou

Abstract

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.

Keywords

laurent polynomial smooth fiber liouville lagrangian skeleton exact symplectic structure rstz skeleton hypertorus

Cite

@article{arxiv.1803.00320,
  title  = {Lagrangian Skeleta of Hypersurfaces in $(\mathbb{C}^*)^n$},
  author = {Peng Zhou},
  journal= {arXiv preprint arXiv:1803.00320},
  year   = {2018}
}

Comments

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

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

Abstract

Keywords

Cite

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