Lagrangian 3-torus fibrations

By Ricardo Casta no Bernard, D. Matessi. 2006

62 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0c85177a221b335bd0985481a25eb0bd9b079847

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In Geometry and Topology

1. L. Katzarkov
2. D. Auroux
3. P. Aspinwall
4. G. Moore
5. T. Bridgeland
6. M. Abouzaid
7. Yukinobu Toda
8. Mark Gross

In Mathematical Physics

1. D. Auroux
2. L. Katzarkov
3. G. Moore
4. Yukinobu Toda
5. M. Abouzaid
6. T. Bridgeland
7. P. Aspinwall
8. A. Kapustin

Citations in the corpus

• Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces (2012, methodology): “This fibration is analogous to some of the examples considered in [18, 19, 6, 7]; see also Example 3.”
• Dirichlet Branes and Mirror Symmetry (2009, background): “In fact, in this case the compactification can be carried out in the symplectic category (see [435, 90]) but we will not give details here.”