Mirror symmetry for toric Fano manifolds via SYZ transformations

Abstract

We construct and apply Strominger-Yau-Zaslow mirror transformations to understand the geometry of the mirror symmetry between toric Fano manifolds and Landau-Ginzburg models.

v4: final version, to appear in Adv. Math.; v3: 38 pages, substantially revised and expanded, the role of tropical geometry clarified in the newly added Subsection 2.2

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Cited by in corpus (28)

• The Coherent-Constructible Correspondence and Homological Mirror Symmetry for Toric Varieties
• Non-Kaehler SYZ mirror symmetry
• T-Duality and Homological Mirror Symmetry of Toric Varieties
• The Ooguri-Vafa metric, holomorphic discs and wall-crossing
• Mirror maps equal SYZ maps for toric Calabi-Yau surfaces
• Lagrangian Floer theory on compact toric manifolds: survey
• Holomorphic line bundles on projective toric manifolds from Lagrangian sections of their mirrors by SYZ transformations
• Homological mirror symmetry for $A_n$-resolutions as a $T$-duality
• Scattering diagrams from asymptotic analysis on Maurer-Cartan equations
• Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces
• A formula equating open and closed Gromov-Witten invariants and its applications to mirror symmetry
• On SYZ mirror transformations
• Matrix factorizations from SYZ transformations
• A relation for Gromov-Witten invariants of local Calabi-Yau threefolds
• Homological mirror symmetry for punctured spheres
• Examples of Matrix Factorizations from SYZ
• SYZ mirror symmetry for toric varieties
• SYZ transforms for immersed Lagrangian multi-sections
• Tropical counting from asymptotic analysis on Maurer-Cartan equations
• Homological mirror symmetry is T-duality for ${\mathbb{P}}^n$
• Homological mirror symmetry and Fourier-Mukai transform
• Tropical Lagrangian multi-sections and toric vector bundles
• Moduli of Lagrangian immersions with formal deformations
• The Strominger-Yau-Zaslow conjecture and its impact
• Quasimap SYZ for toric Calabi-Yau manifolds
• Homological mirror symmetry for local Calabi-Yau manifolds via SYZ
• SYZ mirror symmetry from Witten-Morse theory
• Calabi-Yau components in general type hypersurfaces