\(G_2\)-Grassmannians and derived equivalences. (English) Zbl 1440.14096

Summary: 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 A. Kuznetsov [J. Math. Soc. Japan 70, No. 3, 1007–1013 (2018; Zbl 1423.14128)] closely.


14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
14J32 Calabi-Yau manifolds (algebro-geometric aspects)


Zbl 1423.14128
Full Text: DOI arXiv


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