Derived equivalences for the flops of type $C_2$ and $A_4^G$ via mutation of semiorthogonal decomposition

Abstract

We give a new proof of the derived equivalence of a pair of varieties connected by the flop of type $C_2$ in the list of Kanemitsu arXiv:1812.05392, which is originally due to Segal. 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 $\text{Gr}(2,5)$ and $\text{Gr}(3,5)$ by Kapustka and Rampazzo arXiv:1711.10231 closely.

12 pages; v3: Final version, Minor changes from v2, To appear in Algebra Represent. Theory, DOI:10.1007/s10468-021-10036-y