In this article, we consider the phenomenon of complete coincidence of the key properties of pairs of Calabi-Yau manifolds realized as hypersurfaces in two different weighted projective spaces. More precisely, the first manifold in such a pair is realized as a hypersurface in a weighted projective space, and the second as a hypersurface in the orbifold of another weighted projective space. The two manifolds in each pair have the same Hodge numbers and special Kahler geometry on the complex structure moduli space and are associated with the same $N=2$ gauge linear sigma model. We give the explanation of this interesting coincidence using the Batyrev's correspondence between Calabi-Yau manifolds and the reflexive polyhedra.

中文翻译：

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Berglund-Hübsch 型 Calabi-Yau 流形与 Batyrev 多胞体之间的巧合

在本文中，我们考虑了在两个不同加权射影空间中实现为超曲面的 Calabi-Yau 流形对的关键性质完全重合的现象。更准确地说，这对流形中的第一个流形被实现为加权射影空间中的超曲面，而第二个流形实现为另一个加权射影空间的 orbifold 中的超曲面。每对中的两个流形在复杂结构模空间上具有相同的霍奇数和特殊的 Kahler 几何，并且与相同的 $N=2$ 规范线性 sigma 模型相关联。我们使用 Calabi-Yau 流形和自反多面体之间的 Batyrev 对应关系来解释这个有趣的巧合。