Lagrangian Torus Fibrations and Homological Mirror Symmetry for the Conifold

2013/05/31 by Kwokwai Chan, Daniel Pomerleano, Kazushi Ueda · 25 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conifold #Conjecture #Geometry #Homotopy and Cohomology in Algebraic Topology #Lagrangian #Mathematical physics #Mathematics #Mirror symmetry #Physics #Point (geometry) #Pure mathematics #Symmetry (geometry) #Torus #math.AG #math.SG

paper · pdf · doi:10.1007/s00220-015-2477-7

published in Communications in Mathematical Physics 341(1), 135-178 (Springer Science+Business Media) · 46 pages, 22 figures, v4: corrected an error in the explicit formula for the uncompleted SYZ mirror $Y_0^{\vee}$ in the published version of this paper; we thank Luis Diogo for discussions which lead us to the discovery of this error

openalex publication_date 2015/10/26 · arxiv created 2016/01/07 · arxiv updated 2016/01/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We discuss homological mirror symmetry for the conifold from the point of view of the Strominger-Yau-Zaslow conjecture.

Citations

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• McKay equivalence for symplectic resolutions of singularities
• Suspending Lefschetz Fibrations, with an Application to Local Mirror Symmetry
• Mirror symmetry is T-duality
• Floer cohomology in the mirror of the projective plane and a binodal cubic curve
• Exact Lefschetz fibrations associated with dimer models
• On global action‐angle coordinates
• Introduction to A-infinity algebras and modules

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• Splitting symplectic monodromy