Potential functions via toric degenerations

2008/11/29 by Takeo Nishinou, Nishinou, Takeo, Yuichi Nohara +3 · 1 citation
Mathematics · Physics and Astronomy · #53D12 #53D40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG) #math.AG #math.SG #msc:53D12 #msc:53D40

paper · pdf · doi:10.48550/arxiv.0812.0066

14 pages, no figures. v2: removed errors from an earlier version of arXiv:0810.3470, and added discussions on quadric surface

openalex publication_date 2008/11/29 · arxiv created 2010/02/28 · arxiv updated 2010/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a short companion paper to arXiv:0810.3470. We construct an integrable system on an open subset of a Fano manifold equipped with a toric degeneration, and compute the potential function for its Lagrangian torus fibers if the central fiber is a toric Fano variety admitting a small resolution.

Citations

• Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds
• Lagrangian Floer theory on compact toric manifolds II : Bulk deformations
• Toric degenerations of Gelfand-Cetlin systems and potential functions

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