Abstract
We prove that Mark Gross' [8] topological Calabi-Yau compactifications can be made into symplectic compactifications. To prove this we develop a method to construct singular Lagrangian 3-torus fibrations over certain a priori given integral affine manifolds with singularities, which we call simple. This produces pairs of compact symplectic 6-manifolds homeomorphic to mirror pairs of Calabi-Yau 3-folds together with Lagrangian fibrations whose underlying integral affine structures are dual.
Citation
Ricardo Castaño Bernard. Diego Matessi. "Lagrangian 3-torus fibrations." J. Differential Geom. 81 (3) 483 - 573, March 2009. https://doi.org/10.4310/jdg/1236604343
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