Open Gromov-Witten invariants and SYZ under local conifold transitions

Abstract

For a local Calabi-Yau manifold which is a smoothing of toric Gorenstein singularity, this paper computes the open Gromov-Witten invariants of a generic fiber of the special Lagrangian fibration constructed by Gross and thereby constructs its SYZ mirror. Moreover it derives a relation for the generating function of open Gromov-Witten invariants of the local Calabi-Yau manifold and that of its conifold transition.

v2: minor improvement on exposition. 23 pages, 12 figures

References in corpus (5)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Minkowski Polynomials and Mutations
• Disk enumeration on the quintic 3-fold
• Lagrangian torus fibrations and homological mirror symmetry for the conifold
• Toric degeneration and non-displaceable Lagrangian tori in $S^2\times S^2$

Cited by in corpus (8)

• Noncommutative homological mirror functor
• Immersed two-spheres and SYZ with Application to Grassmannians
• Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}
• $A_n$-type surface singularity and nondisplaceable Lagrangian tori
• Disk counting and wall-crossing phenomenon via family Floer theory
• Geometric transitions and SYZ mirror symmetry
• SYZ mirror symmetry for hypertoric varieties
• Affine elliptic surfaces with type-A singularities and orbi-conifolds