Symmetries of Lagrangian fibrations |
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Authors: | Ricardo Castaño-Bernard Jake P Solomon |
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Institution: | a Mathematics Department, Kansas State University, 138 Cardwell Hall, Manhattan, KS 66506, USA b Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale, Via T. Michel 11, I-15121 Alessandria, Italy c Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, 91904, Israel |
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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 six-dimensional examples constructed by Castaño-Bernard and Matessi (2009) 8], 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. |
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Keywords: | Symplectic manifolds Calabi-Yau manifolds Lagrangian fibrations Homological mirror symmetry |
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