Mirror symmetry without corrections

Abstract

We give geometric explanations and proofs of various mirror symmetry conjectures for $T^n$-invariant Calabi-Yau manifolds when instanton corrections are absent. This uses fiberwise Fourier transformation together with base Legendre transformation. We discuss mirror transformations of (i) moduli spaces of complex structures and complexified symplectic structures, $H^{p,q}$'s, Yukawa couplings; (ii) sl(2)xsl(2)-actions; (iii) holomorphic and symplectic automorphisms and (iv) A- and B-connections, supersymmetric A- and B-cycles, correlation functions. We also study (ii) for $T^n$-invariant hyperkahler manifolds.

Corrected version

References in corpus (2)

• Nonlinear Instantons from Supersymmetric p-Branes
• Lectures on Special Lagrangian Submanifolds

Cited by in corpus (9)

• Homogeneous coordinate rings and mirror symmetry for toric varieties
• Special Lagrangian fibrations, mirror symmetry and Calabi-Yau double covers
• Examples of Special Lagrangian Fibrations
• Convergence of Hermitian-Yang-Mills Connections on Kähler Surfaces and mirror symmetry
• Singular Semi-Flat Calabi-Yau Metrics on S^2
• Limiting behavior of local Calabi-Yau metrics
• Large Radius Limit and SYZ Fibrations of Hyper-Kahler Manifolds
• Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition
• Riemannian geometry over different normed division algebra