On bicanonical maps of threefolds of general type with large volumes

Abstract: We prove that for any smooth projective $3$-fold of general type with canonical volume greater than $12^6$, the image of its bicanonical map has dimension at least $2$. We also study pluricanonical maps of $3$-folds of general type with large canonical volume and fibered by $(1,2)$-surfaces or $(2,3)$-surfaces.