By generalizing the Landau–Ginzburg/Calabi–Yau correspondence for hypersurfaces, we can relate a Calabi–Yau complete intersection to a hybrid Landau–Ginzburg model: a family of isolated singularities fibered over a projective line. In recent years Fan, Jarvis, and Ruan have defined quantum invariants for singularities of this type, and Clader and Clader–Ross have provided an equivalence between these invariants and Gromov–Witten invariants of complete intersections, in this way quantum cohomology yields an identification of the cohomology groups of the Calabi–Yau and of the hybrid Landau–Ginzburg model. It is not clear how to relate this to the known isomorphism descending from derived equivalences (due to Segal and Shipman, and Orlov and Isik). We answer this question for Calabi–Yau complete intersections of two cubics.

中文翻译：

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Landau-Ginzburg/Calabi-Yau 对应通过矩阵分解的完全交集

通过推广超曲面的 Landau-Ginzburg/Calabi-Yau 对应关系，我们可以将 Calabi-Yau 完全交集与混合 Landau-Ginzburg 模型联系起来：在投影线上纤维化的孤立奇点族。近年来 Fan、Jarvis 和 Ruan 已经为这类奇点定义了量子不变量，Clader 和 Clader-Ross 提供了这些不变量与完全交的 Gromov-Witten 不变量之间的等价性，通过这种方式，量子上同调产生了Calabi-Yau 和混合 Landau-Ginzburg 模型的上同调群。目前尚不清楚如何将其与派生等价的已知同构联系起来（由于 Segal 和 Shipman，以及 Orlov 和 Isik）。我们为两个立方的 Calabi-Yau 完全交集回答了这个问题。