Pluricanonical maps of minimal 3-folds (Q1079621)

The author studies pluricanonical maps of smooth threefolds over the field of complex numbers under the condition that they have minimal models. He gives an outline of the proof of the following theorem: Let X be a minimal threefold of general type with \(index\quad r\) and let \(K_ X\) denote the canonical divisor. Then the n-ple pluricanonical map \(F_{| nK_ X|}\) is birational for \(n\geq n_ 0\) where \(n_ 0=9\) if \(r=1\); \(n_ 0=8\) if \(r=1\) and if X is Q-factorial; \(n_ 0=13\) if \(r=2\); \(n_ 0=4r+4\) if \(3\leq r\leq 5\); \(n_ 0=4r+3\) if \(r\geq 6\).