Derived equivalences for the flops of type C₂ and A^G₄ via mutation of semiorthogonal decomposition

2018/12/16 by Hayato Morimura, Morimura, Hayato
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1812.06413

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

arxiv created 2021/03/03 · arxiv updated 2021/03/04

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 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^G₄ 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 arXiv:1711.10231 closely.

Citations

• Mukai pairs and simple K-equivalence
• Torelli problem for Calabi-Yau threefolds with GLSM description

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