For special cubic fourfolds that are Fourier-Mukai partners, transcendental motives are isomorphic, with explicit descriptions in Hassett divisor families and for those with order-3 automorphisms.
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Kuznetsov components and transcendental motives of cubic fourfolds
For special cubic fourfolds that are Fourier-Mukai partners, transcendental motives are isomorphic, with explicit descriptions in Hassett divisor families and for those with order-3 automorphisms.