We present a new construction of mirror pairs of Calabi–Yau manifolds by smoothing normal crossing varieties, consisting of two quasi-Fano manifolds. We introduce a notion of mirror pairs of quasi-Fano manifolds with anticanonical Calabi–Yau fibrations using recent conjectures about Landau–Ginzburg models. Utilizing this notion, we give pairs of normal crossing varieties and show that the pairs of smoothed Calabi–Yau manifolds satisfy the Hodge number relations of mirror symmetry. We consider quasi-Fano threefolds that are some blow-ups of Gorenstein toric Fano threefolds and build 6518 mirror pairs of Calabi–Yau threefolds, including 79 self-mirrors.

我们通过平滑由两个准-Fano流形组成的正常穿越品种，提出了一种新的对Calabi–Yau流形镜像对的构造。我们使用关于Landau-Ginzburg模型的最新猜想，引入了具有反规范的Calabi-Yau纤维的准Fano流形的镜像对的概念。利用该概念，我们给出了成对的正交变种，并证明了成对的光滑的Calabi-Yau流形满足镜像对称的霍奇数关系。我们将准Fano三倍视为Gorenstein复曲面Fano的爆炸，并构建6518对Calabi–Yau三倍镜像，包括79个自镜像。