Symmetries of Lagrangian fibrations
Symplectic Geometry
2012-01-19 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0908.0966,
title = {Symmetries of Lagrangian fibrations},
author = {Ricardo Castaño-Bernard and Diego Matessi and Jake P. Solomon},
journal= {arXiv preprint arXiv:0908.0966},
year = {2012}
}
Comments
45 pages