Fourier–Mukai partners for very general special cubic fourfolds

We exhibit explicit examples of very 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 very general special cubic fourfold 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 $d \equiv 2 (\operatorname{mod} 6)$; else, if $d \equiv 0 (\operatorname{mod} 6)$, the cubic fourfold has $\lceil m / 2 \rceil$ Fourier–Mukai partners.

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Received 5 March 2019

Accepted 3 August 2019

Published 24 May 2022