Fourier-Mukai partners for very general special cubic fourfolds

Abstract

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 $d\equiv 2(\text{mod}6)$; else, if $d\equiv 0(\text{mod}6)$, the cubic fourfold has $\lceil m/2\rceil$ Fourier-Mukai partners.

arXiv comment20 pages, Final version to appear in Math. Research Letters