For smooth projective threefolds of general type with vol(K_X) > 12^6 the bicanonical map has image of dimension at least 2.
Chen,On an efficient induction step with Nklt(X, D)—notes to Todorov, Comm
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On bicanonical maps of threefolds of general type with large volumes
For smooth projective threefolds of general type with vol(K_X) > 12^6 the bicanonical map has image of dimension at least 2.