Dual torus fibrations and homological mirror symmetry for A_n-singularities

Abstract

We study homological mirror symmetry for not necessarily compactly supported coherent sheaves on the minimal resolutions of A_n-singularities. An emphasis is put on the relation with the Strominger-Yau-Zaslow conjecture.

v3: major revision; 27 pages, 12 figures

References in corpus (6)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry
• Lagrangian torus fibrations and homological mirror symmetry for the conifold
• Dimer models and exceptional collections
• Homological mirror symmetry for $A_n$-resolutions as a $T$-duality
• Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces

Cited by in corpus (10)

• On the symplectic cohomology of log Calabi-Yau surfaces
• Lagrangian torus fibrations and homological mirror symmetry for the conifold
• Lagrangian pairs of pants
• Open Gromov-Witten invariants and SYZ under local conifold transitions
• Classification of Rank 2 Cluster Varieties
• SYZ transforms for immersed Lagrangian multi-sections
• Families of monotone Lagrangians in Brieskorn--Pham hypersurfaces
• Homological mirror symmetry for local Calabi-Yau manifolds via SYZ
• The Strominger-Yau-Zaslow conjecture and its impact
• Symplectomorphisms of some Weinstein 4-manifolds