Abstract
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.
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Acknowledgements
The author would like to express his gratitude to Kazushi Ueda for guidance and encouragement. The author would like to thank anonymous reviewers for their careful reading of the manuscript and their many suggestions and comments. The author declare that he has no conflict of interest.
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Presented by: Michel Van den Bergh
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Morimura, H. Derived Equivalences for the Flops of Type C2 and \({A}_{4}^{G}\) via Mutation of Semiorthogonal Decomposition. Algebr Represent Theor 25, 581–594 (2022). https://doi.org/10.1007/s10468-021-10036-y
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DOI: https://doi.org/10.1007/s10468-021-10036-y