Lagrangian torus fibrations and homological mirror symmetry for the conifold

Abstract

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

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

References in corpus (4)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• On the symplectic cohomology of log Calabi-Yau surfaces
• Infinitely many monotone Lagrangian tori in ${\mathbb{R}}^6$
• Mixed braid group actions from deformations of surface singularities

Cited by in corpus (17)

• Lagrangian pairs of pants
• Immersed two-spheres and SYZ with Application to Grassmannians
• Open Gromov-Witten invariants and SYZ under local conifold transitions
• Mixed braid group actions from deformations of surface singularities
• Lagrangian sections on mirrors of toric Calabi-Yau 3-folds
• SYZ transforms for immersed Lagrangian multi-sections
• Homological Mirror Symmetry for local SYZ singularities
• Potential functions on Grassmannians of planes and cluster transformations
• Perverse schobers on Riemann surfaces: constructions and examples
• Local mirror symmetry via SYZ
• The Strominger-Yau-Zaslow conjecture and its impact
• Symplectomorphisms and spherical objects in the conifold smoothing
• Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties
• SYZ mirror symmetry for hypertoric varieties
• Homological mirror symmetry for local Calabi-Yau manifolds via SYZ
• Affine elliptic surfaces with type-A singularities and orbi-conifolds
• Maurer-Cartan deformation of Lagrangians