2014/08/31 by John Calabrese, John R. Calabrese, Richard P. Thomas · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Complete intersection #Cubic form #Cubic function #Geometric and Algebraic Topology #Intersection (aeronautics) #Pencil (optics) #math.AG
paper · pdf · doi:10.1007/s00208-015-1260-6
published as Math. Ann. 365, 155-172, 2016 · referee's corrections
openalex publication_date 2015/08/03 · arxiv created 2015/09/10 · arxiv updated 2016/06/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We describe pretty examples of derived equivalences and autoequivalences of Calabi-Yau threefolds arising from pencils of cubic fourfolds. The cubic fourfolds are chosen to be special, so they have an associated K3 surface. Thus a pencil gives rise to two different Calabi-Yau threefolds: the associated pencil of K3 surfaces, and the baselocus of the original pencil - the intersection of two cubic fourfolds. They both have crepant resolutions which are derived equivalent.