Lagrangian torus fibration and mirror symmetry of Calabi-Yau hypersurface in toric variety

Abstract

In this paper we give a construction of Lagrangian torus fibration for Calabi-Yau hypersurface in toric variety via the method of gradient flow. Using our construction of Lagrangian torus fibration, we are able to prove the symplectic topological version of SYZ mirror conjecture for generic Calabi-Yau hypersurface in toric variety. We will also be able to give precise formulation of SYZ mirror conjecture in general (including singular locus and duality of singular fibres).

60 pages. More references will be added later

References in corpus (1)

• The moduli space of special Lagrangian submanifolds

Cited by in corpus (9)

• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Lectures on Calabi-Yau and special Lagrangian geometry
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• Examples of Special Lagrangian Fibrations
• Instanton amplitudes in open-closed topological string theory
• Lagrangian torus fibration of quintic Calabi-Yau hypersurfaces I: Fermat quintic case
• Singularities of special Lagrangian fibrations and the SYZ Conjecture
• Special Lagrangian torus fibrations of complete intersection Calabi-Yau manifolds: a geometric conjecture