Some birationality criteria on 3-folds with \(p_g>1\) (Q487485)

There are quite a bit of interests in studying the explicit birational geometry of 3-folds. The current paper under review studies the following question: Given a 3-fold \(X\) of general type, when is the pluricanonical map induced by \(|m K_X|\) a birational map? An explicit bound depends on the volume of the canonical divisor and the geometric genus. The author provides some birationality crieria when the geometric genus is at least \(2\) by an intensive classification.