2000/07/05 by Wei-Dong Ruan, Ruan, Wei-Dong · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.AG #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.math/0007028
60 pages. More references will be added later
arxiv created 2000/07/05 · openalex publication_date 2000/07/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give a construction of Lagrangian torus fibration for Calabi-Yau hypersurface in toric variety via the method of gradient flow. Using our construction of Lagrangian torus fibration, we are able to prove the symplectic topological version of SYZ mirror conjecture for generic Calabi-Yau hypersurface in toric variety. We will also be able to give precise formulation of SYZ mirror conjecture in general (including singular locus and duality of singular fibres).