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

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

2000-07-05

arxiv.org/abs/math/0007028v1

Mathematics

Differential Geometry

60 pages. More references will be added later

Scientific paper

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).

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