Journal of Differential Geometry

Lagrangian 3-torus fibrations

Ricardo Castaño Bernard and Diego Matessi

Full-text: Open access

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.

Article information

Source
J. Differential Geom. Volume 81, Number 3 (2009), 483-573.

Dates
First available in Project Euclid: 9 March 2009

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1236604343

Digital Object Identifier
doi:10.4310/jdg/1236604343

Mathematical Reviews number (MathSciNet)
MR2487600

Zentralblatt MATH identifier
1177.14080

Citation

Castaño Bernard, Ricardo; Matessi, Diego. Lagrangian 3-torus fibrations. J. Differential Geom. 81 (2009), no. 3, 483--573. doi:10.4310/jdg/1236604343. https://projecteuclid.org/euclid.jdg/1236604343.


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