6-canonical maps of nonsingular minimal 3-folds (Q1893420)

Let \(X\) be a complex nonsingular projective threefold whose canonical divisor is nef and big. It is known that the map \(\varphi_n\) associated to the linear system \(|nK_X |\) is birational for \(n\geq 7\). -- In this note the author studies the case \(n=6\) under the assumption that \(|2K_X |\) is not composed with a pencil. He proves that \(\varphi_6\) is also birational, with two possible exceptions.