Fourier-Mukai partners for general special cubic fourfolds

We exhibit explicit examples of general special cubic fourfolds with discriminant d admitting an associated (twisted) K3 surface, which have non-isomorphic Fourier-Mukai partners. In particular, in the untwisted setting, we show that the number of Fourier-Mukai partners for a general cubic fourfold in the moduli space of special cubic fourfolds with discriminant d and having an associated K3 surface, is equal to the number m of Fourier-Mukai partners of its associated K3 surface, if d ” 2pmod 6q; else, if d ” 0pmod 6q, the cubic fourfold has rm{2s Fourier-Mukai partners.

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