Derived equivalences for the flops of type $C_2$ and $A^G_4$ via mutation of semiorthogonal decomposition

Hayato Morimura

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arXiv · 1812.06413

Derived equivalences for the flops of type $C_2$ and $A^G_4$ via mutation of semiorthogonal decomposition

Hayato Morimura

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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 $A^G_4$ 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.

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Hayato Morimura. 2018-12-16. Derived equivalences for the flops of type $C_2$ and $A^G_4$ via mutation of semiorthogonal decomposition. https://arxiv.org/abs/1812.06413

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