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Calabi-Yau components in general type hypersurfaces

Conan Leung Chinese Univ of HK Tom Wan Chinese Univ of HK

mathscidoc:1608.01055

Journal of Differential Geometry, 83, 43-74, 2009
For a one-parameter family (V, \Omega_{i}) with I=1,...,p_g of general type hypersurfaces with bases of holomorphic n-forms, we construct open covers V = Spg i=1 Ui using tropical geometry. We show that after normalization, each i is approximately supported on a unique Ui and such a pair approximates a Calabi-Yau hypersurface together with its holomorphic n-form as the parameter becomes large. We also show that the Lagrangian fibers in the fibration constructed by Mikhalkin [9] are asymptotically special Lagrangian. As the holomorphic n-form plays an important role in mirror symmetry for Calabi-Yau manifolds, our results is a step toward understanding mirror symmetry for general type manifolds.
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@inproceedings{conan2009calabi-yau,
  title={Calabi-Yau components in general type hypersurfaces},
  author={Conan Leung, and Tom Wan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160830144348375906561},
  booktitle={Journal of Differential Geometry},
  volume={83},
  pages={43-74},
  year={2009},
}
Conan Leung, and Tom Wan. Calabi-Yau components in general type hypersurfaces. 2009. Vol. 83. In Journal of Differential Geometry. pp.43-74. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160830144348375906561.
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