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.
| Original language | English |
|---|---|
| Pages (from-to) | 483-573 |
| Number of pages | 91 |
| Journal | Journal of Differential Geometry |
| Volume | 81 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2009 |
ASJC Scopus Subject Areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology
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