Mirror Symmetry of Fourier MukaitransformationforEllipticCalabi Yau manifolds

Naichung Conan Leung Shing-Tung Yau

Symplectic Geometry mathscidoc:1912.43663

2007.5
Mirror symmetry conjecture identifies the complex geometry of a Calabi $ Yau manifold with the symplectic geometry of its mirror Calabi $ Yau man $ ifold. Using the SYZ mirror transform, we argue that (i) the mirror of an elliptic Calabi $ Yau manifold admits a twin Lagrangian fibration structure and (ii) the mirror of the Fourier $ Mukai transform for dual elliptic fibra $ tions is a symplectic Fourier $ Mukai transform for dual twin Lagrangian fibrations, which is essentially an identity transformation in this case.
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@inproceedings{naichung2007mirror,
  title={Mirror Symmetry of Fourier MukaitransformationforEllipticCalabi Yau manifolds},
  author={Naichung Conan Leung, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204820095415227},
  year={2007},
}
Naichung Conan Leung, and Shing-Tung Yau. Mirror Symmetry of Fourier MukaitransformationforEllipticCalabi Yau manifolds. 2007. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204820095415227.
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