Lagrangian 3-torus fibrations

Details Lagrangian 3-torus fibrations Lagrangian 3-torus fibrations

2006-11-06

arxiv.org/abs/math/0611139v1

J. Differential Geom. 81 (2009), no. 3, 483--573

Mathematics

Symplectic Geometry

68 pages, 17 figures

Scientific paper

We give a method to construct singular Lagrangian 3-torus fibrations over certain a priori given integral affine manifolds with singularities, which we call simple. The main result of this article is the proof that the topological Calabi-Yau compactifications of M. Gross' "Topological Mirror Symmetry", can be made into symplectic compactifications. As an example, we obtain a pair of compact symplectic 6-manifolds together with Lagrangian fibrations whose underlying affine structures are dual. The symplectic manifolds obtained are homeomorphic to a smooth quintic Calabi-Yau 3-fold and its mirror.

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