Lagrangian 3-torus fibrations

Ricardo Castano Bernard Kansas State University Diego Matessi Universit`a del Piemonte Orientale

Differential Geometry mathscidoc:1609.10106

Journal of Differential Geometry, 81, (3), 483-573, 2009
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.
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@inproceedings{ricardo2009lagrangian,
  title={LAGRANGIAN 3-TORUS FIBRATIONS},
  author={Ricardo Castano Bernard, and Diego Matessi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911180530034263763},
  booktitle={Journal of Differential Geometry},
  volume={81},
  number={3},
  pages={483-573},
  year={2009},
}
Ricardo Castano Bernard, and Diego Matessi. LAGRANGIAN 3-TORUS FIBRATIONS. 2009. Vol. 81. In Journal of Differential Geometry. pp.483-573. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911180530034263763.
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