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Maximal families of Calabi-Yau manifolds with minimal length Yukawa coupling

Mao Sheng School of Mathematical Sciences, University of Science and Technology of China Jinxing Xu School of Mathematical Sciences, University of Science and Technology of China Kang Zuo Institut für Mathematik, Universität Mainz

mathscidoc:1811.01001

Distinguished Paper Award in 2018

Communications in Mathematics and Statistics, 1, (1), 73-92, 2013.3
For each natural odd number n ≥ 3, we exhibit a maximal family of n-dimensional Calabi–Yau manifolds whose Yukawa coupling length is 1. As a consequence, Shafarevich’s conjecture holds true for these families. Moreover, it follows from Deligne and Mostow (Publ. Math. IHÉS, 63:5–89, 1986) and Mostow (Publ. Math. IHÉS, 63:91–106, 1986; J. Am. Math. Soc., 1(3):555–586, 1988) that, for n = 3, it can be partially compactified to a Shimura family of ball type, and for n = 5,9, there is a sub Q-PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient
Calabi-Yau, Yukawa coupling, Hodge theory
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@inproceedings{mao2013maximal,
  title={Maximal families of Calabi-Yau manifolds with minimal length Yukawa coupling},
  author={Mao Sheng, Jinxing Xu, and Kang Zuo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181101151226953863172},
  booktitle={Communications in Mathematics and Statistics},
  volume={1},
  number={1},
  pages={73-92},
  year={2013},
}
Mao Sheng, Jinxing Xu, and Kang Zuo. Maximal families of Calabi-Yau manifolds with minimal length Yukawa coupling. 2013. Vol. 1. In Communications in Mathematics and Statistics. pp.73-92. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181101151226953863172.
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