Symmetries of Lagrangian fibrations
arXiv:0908.0966 · doi:10.1016/j.aim.2010.04.001
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.
45 pages
References in corpus (7)
- Mirror symmetry and T-duality in the complement of an anticanonical divisor
- Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
- Disk enumeration on the quintic 3-fold
- Microlocal branes are constructible sheaves
- Almost toric symplectic four-manifolds
- Involutions, obstructions and mirror symmetry
- Semi-global invariants of piecewise smooth Lagrangian fibrations
Cited by in corpus (12)
- Anti-symplectic involution and Floer cohomology
- Involutions, obstructions and mirror symmetry
- Real Lagrangians in Calabi-Yau Threefolds
- Versality of the relative Fukaya category
- Floer cohomology of real Lagrangians in the Fermat quintic threefold
- On the cohomology groups of real Lagrangians in Calabi-Yau threefolds
- Versality in mirror symmetry
- Family Floer mirror space for local SYZ singularities
- On real Calabi-Yau threefolds twisted by a section
- A Note on Schoen's Calabi--Yau Threefolds
- Family Floer superpotential's critical values are eigenvalues of quantum product by
- Mirror symmetry for tropical hypersurfaces and patchworking