  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.
