We consider the multiple Calabi–Yau mirror phenomenon which appears in Berglund–Hübsch–Krawitz (BHK) mirror symmetry. We show that for any pair of Calabi–Yau orbifolds that are BHK mirrors of a loop–chain-type pair of Calabi–Yau threefolds in the same weighted projective space the periods of the holomorphic nonvanishing form coincide.

中文翻译：

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多个 Berglund-Hübsch-Krawitz 反射镜的周期

我们考虑出现在 Berglund-Hübsch-Krawitz (BHK) 镜像对称中的多重 Calabi-Yau 镜像现象。我们表明，对于任何一对 Calabi-Yau 轨道，它们是同一加权射影空间中环链型 Calabi-Yau 三重的 BHK 镜像，全纯非零形式的周期重合。