On the birationality of the bicanonical map of a surface section of a threefold

Let (M,L) be a polarized threefold of log-general type. The birationality of the bicanonical map of a smooth surface S \in |L| is studied. This problem was previously considered and partially solved by the first and the fourth author, who gave a satisfactory classification unless h^1(\Cal O_M)=0 and p_g(S)=3,4,5. This article focuses on the remaining cases which are the hardest, settling the problem