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 six-dimensional examples constructed by Castaño-Bernard and Matessi (2009) , which include a six-dimensional symplectic manifold homeomorphic to 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.
|Titolo:||Symmetries of Lagrangian fibrations|
MATESSI, DIEGO (Secondo)
|Parole Chiave:||Symplectic manifolds ; Calabi–Yau manifolds ; Lagrangian fibrations ; Homological mirror symmetry|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||ott-2010|
|Digital Object Identifier (DOI):||10.1016/j.aim.2010.04.001|
|Appare nelle tipologie:||01 - Articolo su periodico|