Lagrangian 3-torus fibrations
Symplectic Geometry
2009-08-07 v1 Algebraic Geometry
Abstract
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 the topological Calabi-Yau compactifications of M. Gross' "Topological Mirror Symmetry", 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 are homeomorphic to a smooth quintic Calabi-Yau 3-fold and its mirror.
Cite
@article{arxiv.math/0611139,
title = {Lagrangian 3-torus fibrations},
author = {R. Castano-Bernard and D. Matessi},
journal= {arXiv preprint arXiv:math/0611139},
year = {2009}
}
Comments
68 pages, 17 figures