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We prove the derived equivalence of a pair of non-compact Calabi–Yau 7-folds, which are the total spaces of certain rank 2 bundles on \(G_2\)-Grassmannians. The proof follows that of the derived equivalence of Calabi–Yau 3-folds in \(G_2\)-Grassmannians by Kuznetsov (Derived equivalence of Ito–Miura–Okawa–Ueda Calabi–Yau 3-folds. arXiv:1611.08386) closely.

$$G_2$$-Grassmannians and derived equivalences