Derived equivalent Calabi-Yau threefolds from cubic fourfolds

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 each 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.