Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}

Abstract

This paper gives a new way of constructing Landau-Ginzburg mirrors using deformation theory of Lagrangian immersions motivated by the works of Seidel, Strominger-Yau-Zaslow and Fukaya-Oh-Ohta-Ono. Moreover we construct a canonical functor from the Fukaya category to the mirror category of matrix factorizations. This functor derives homological mirror symmetry under some explicit assumptions. As an application, the construction is applied to spheres with three orbifold points to produce their quantum-corrected mirrors and derive homological mirror symmetry. Furthermore we discover an enumerative meaning of the (inverse) mirror map for elliptic curve quotients.

v4: improved expositions, added Theorem 1.3 and more references

References in corpus (11)

• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots
• Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle
• Primitive forms via polyvector fields
• Family Floer cohomology and mirror symmetry
• Gromov-Witten theory of elliptic orbifold P^1 and quasi-modular forms
• Landau-Ginzburg/Calabi-Yau Correspondence of all Genera for Elliptic Orbifold $p^1$
• Homological Mirror Symmetry and Simple Elliptic Singularities
• Lagrangian Floer potential of orbifold spheres
• Primitive Forms for Affine Cusp Polynomials
• Localized mirror functor constructed from a Lagrangian torus
• Finite group actions on Lagrangian Floer theory

Cited by in corpus (7)

• Lagrangian Floer potential of orbifold spheres
• Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry
• Localized mirror functor constructed from a Lagrangian torus
• Pairings in mirror symmetry between a symplectic manifold and a Landau-Ginzburg $B$-model
• Equivariant split generation and mirror symmetry of special isogenous tori
• Superfiltered $A_{\infty }$-deformations of the exterior algebra, and local mirror symmetry
• Twin Lagrangian fibrations in mirror symmetry