On the birationality of adjunction mappings (Q1340192)

Let \(\Phi_ m\) be the rational map associated to the adjoint linear system \(| K_ X + mD |\) on a nonsingular projective variety \(X\). If \(D\) is a nef and big divisor satisfying certain conditions, we shall give an explicit lower bound for \(m\) for which \(\Phi_ m\) is a birational map. The proof is by induction on the dimension of \(X\) using the results on the effective base point freeness due to J. Kollár and Ein-Lazarsfeld.