Mirror symmetry for toric Fano manifolds via SYZ transformations

DOI10.1016/j.aim.2009.09.009zbMath1201.14029arXiv0801.2830OpenAlexW2035199656MaRDI QIDQ2655793

Naichung Conan Leung, Kwokwai Chan

Publication date: 26 January 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.2830

zbMATH Keywords

mirror symmetryT-dualityquantum cohomologyFourier-Mukai transformLagrangian submanifoldMaslov indexsymplectic manifoldSYZ conjectureLandau-Ginzburg modeltropical geometryJacobian ringtoric Fano manifoldSYZ transformationtropical disc

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Fano varieties (14J45) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (53D45) Mirror symmetry (algebro-geometric aspects) (14J33) Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category (53D37)

Related Items

Scattering diagrams from asymptotic analysis on Maurer-Cartan equations ⋮ Lagrangian Floer theory on compact toric manifolds. I. ⋮ Homological mirror symmetry for punctured spheres ⋮ Coregularity of Fano varieties ⋮ \(T\)-equivariant disc potential and SYZ mirror construction ⋮ Tropical Lagrangian multisections and toric vector bundles ⋮ Tropical counting from asymptotic analysis on Maurer-Cartan equations ⋮ T-duality and homological mirror symmetry for toric varieties ⋮ Non-Kähler SYZ mirror symmetry ⋮ Homological mirror symmetry for local Calabi-Yau manifolds via SYZ ⋮ Mirror symmetry for \(\mathbb P^2\) and tropical geometry ⋮ Reconstruction of holomorphic tangent bundle of complex projective plane via tropical Lagrangian multi-section ⋮ Compactifying torus fibrations over integral affine manifolds with singularities ⋮ SYZ transforms for immersed Lagrangian multisections

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