We give a new proof of the derived equivalence of a pair of varieties connected by the flop of type C₂ in the list of Kanemitsu (2018), which is originally due to Segal (Bull. Lond. Math. Soc., 48 (3) 533–538, 2016). We also prove the derived equivalence of a pair of varieties connected by the flop of type \({A}_{4}^{G}\) in the same list. The latter proof follows that of the derived equivalence of Calabi–Yau 3-folds in Grassmannians Gr(2,5) and Gr(3,5) by Kapustka and Rampazzo (Commun. Num. Theor. Phys., 13 (4) 725–761 2019) closely.

中文翻译：

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通过半正交分解的突变获得C 2和A 4 G $ {A} _ {4} ^ {G} $触发器的等效

我们给出了在Kanemitsu（2018）列表中通过C ₂的翻牌连接的一对变体对的等价性的新证明，其最初是由Segal（Bull.Lond.Math.Soc。，48（3 533-538，2016年）。我们还证明了在同一列表中通过类型\（{A} _ {4} ^ {G} \）的翻牌连接的一对变体的导出等价性。后一个证明是由Kapustka和Rampazzo得出的格拉斯曼氏Gr（2,5）和Gr（3,5）的Calabi–Yau 3倍的等价性（Commun。Num。Theor。Phys。，13（4）725）。 –761 2019）。