2021/03/03 by Federico Barbacovi, Barbacovi, Federico
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.2103.02555
The content of this paper was merged into arXiv:2007.14415
openalex publication_date 2021/03/03 · arxiv created 2021/11/02 · arxiv updated 2021/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In arXiv:2007.14415 we proved that the "flop-flop" autoequivalence can be realized as the spherical twist around a spherical functor whose source category arises naturally from the geometry. In this companion paper we study in detail some examples so to explicitly describe what the source category looks like. In some cases we are able to prove that the source category respects the known decomposition of the flop-flop autoequivalence, and therefore we tie up our geometric description with formal results which appear in the literature about gluing and splitting of spherical twists around spherical functors. The examples we treat completely are standard flops (both in the local model and in the family version), and Mukai flops. We also discuss the cases of Grassmannian flops, and the Abuaf flop.