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arXiv · 1211.3646

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

Mao Sheng·Jinxing Xu·Kang Zuo
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Abstract

For each natural odd number $n\geq 3$, we exhibit a maximal family of $n$-dimensional Calabi-Yau manifolds whose Yukawa coupling length is one. As a consequence, Shafarevich's conjecture holds true for these families. Moreover, it follows from Deligne-Mostow and Mostow 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 $\mathbb Q$-PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient.

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Mao Sheng, Jinxing Xu, Kang Zuo. 2012-11-15. Maximal families of Calabi-Yau manifolds with minimal length Yukawa coupling. https://arxiv.org/abs/1211.3646

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