The Fano-fibration degeneration conjecture

Let a Fano fibration be a fibration whose fibres are Fano varieties, possibly with singular fibres in a degeneration. Fano-fibration degeneration conjecture. A Fano fibration is polystable if and only if it is polystable with respect to fibration degenerations whose central fibre is a Fano fibration. This would reduce the testing of polystability for Fano fibrations to degenerations with Fano-fibration central fibre, paralleling the corresponding phenomenon for Fano varieties. The conjecture is presented as a likely analogue and remains open.