Fourier–Mukai partners under specialization

Determine whether the Fourier–Mukai partnership between the cubic fourfolds constructed from the Enriques Cremona transformation persists under simultaneous smooth specialization.

Background

Birationality of the constructed pairs persists under simultaneous smooth specialization by the specialization theorem of Kontsevich–Tschinkel. However, the Enriques surfaces and the common blow-up presentation need not extend to special fibres, so the persistence of the Fourier–Mukai equivalence is not established.