Symmetries of Lagrangian fibrations

Details Symmetries of Lagrangian fibrations Symmetries of Lagrangian fibrations

2009-08-07

arxiv.org/abs/0908.0966v1

Adv. Math. 225 (2010), no. 3, 1341-1386

Mathematics

Symplectic Geometry

45 pages

Scientific paper

10.1016/j.aim.2010.04.001

We construct fiber-preserving anti-symplectic involutions for a large class of symplectic manifolds with Lagrangian torus fibrations. In particular, we treat the K3 surface and the quintic threefold. We interpret our results as corroboration of the view that in homological mirror symmetry, an anti-symplectic involution is the mirror of duality. In the same setting, we construct fiber-preserving symplectomorphisms that can be interpreted as the mirror to twisting by a holomorphic line bundle.

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