We generalize the cohomological mirror duality of Borcea and Voisin in any dimension and for any number of factors. Our proof applies to all examples which can be constructed through Berglund-Hubsch duality. Our method is a variant of the so-called Landau-Ginzburg/Calabi-Yau correspondence of Calabi-Yau orbifolds with an involution that does not preserve the volume form. We deduce a version of mirror duality for the fixed loci of the involution, which are beyond the Calabi-Yau category and feature hypersurfaces of general type.

中文翻译：

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Semi-Calabi-Yau orbifolds 和镜像对

我们将 Borcea 和 Voisin 的上同调镜像二元性在任何维度和任何数量的因素中推广。我们的证明适用于所有可以通过 Berglund-Hubsch 对偶构造的例子。我们的方法是 Calabi-Yau orbifolds 所谓的 Landau-Ginzburg/Calabi-Yau 对应关系的变体，其对合不保留体积形式。我们为对合的固定位点推导出镜像二元性的一个版本，它超出了 Calabi-Yau 类别并具有一般类型的超曲面。