Lagrangian 3-torus fibrations

Ricardo Castaño Bernard, Diego Matessi
2009 Journal of differential geometry  
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 Mark Gross' [7] topological Calabi-Yau compactifications 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
more » ... manifolds obtained are homeomorphic to a smooth quintic Calabi-Yau 3-fold and its mirror.
doi:10.4310/jdg/1236604343 fatcat:6ppec3xb2jepfihvc34nuiik2y