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.

arXiv comment12 pages; v3: Final version, Minor changes from v2, To appear in Algebra Represent. Theory, DOI:10.1007/s10468-021-10036-y

References in corpus (6)

• Semiorthogonal decomposition for algebraic varieties
• Derived categories of coherent sheaves
• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• Exceptional collections for Grassmannians of isotropic lines
• Mukai flops and P-twists
• On derived equivalence for Abuaf flop: mutation of non-commutative crepant resolutions and spherical twists

Cited by in corpus (1)

• Calabi-Yau fibrations, simple K-equivalence and mutations