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Finiteness of subfamilies of Calabi-Yau n-folds over curves with maximal length of Yukawa-coupling

Kefeng Liu Andrey Todorov Shing-Tung Yau Kang Zuo

Mathematical Physics mathscidoc:1912.43660

arXiv preprint arXiv:1010.4141, 2010.10
We give a simplified and more algebraic proof of the finiteness of the families of Calabi-Yau n-folds with non-vanishing of Yukawa-coupling over a fixed base curve and with fixed degeneration locus. We also give a generalization of this result. Our method is variation of Hodge structure and poly-stability of Higgs bundles.
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@inproceedings{kefeng2010finiteness,
  title={Finiteness of subfamilies of Calabi-Yau n-folds over curves with maximal length of Yukawa-coupling},
  author={Kefeng Liu, Andrey Todorov, Shing-Tung Yau, and Kang Zuo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204809147626224},
  booktitle={arXiv preprint arXiv:1010.4141},
  year={2010},
}
Kefeng Liu, Andrey Todorov, Shing-Tung Yau, and Kang Zuo. Finiteness of subfamilies of Calabi-Yau n-folds over curves with maximal length of Yukawa-coupling. 2010. In arXiv preprint arXiv:1010.4141. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204809147626224.
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