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Calabi-yau components in general type hypersurfaces

Naichung Conan Leung The Chinese University of Hong Kong Tom Y.H. Wan The Chinese University of Hong Kong

Differential Geometry mathscidoc:1609.10133

Journal of Differential Geometry, 83, (1), 43-74, 2009
For a one-parameter family (V, {i}pg i=1) 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{naichung2009calabi-yau,
  title={CALABI-YAU COMPONENTS IN GENERAL TYPE HYPERSURFACES},
  author={Naichung Conan Leung, and Tom Y.H. Wan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911194942680769790},
  booktitle={Journal of Differential Geometry},
  volume={83},
  number={1},
  pages={43-74},
  year={2009},
}
Naichung Conan Leung, and Tom Y.H. 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/20160911194942680769790.
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