| Given a smooth projective variety X, one has the pluricanonical line bundles £s for free. If the pluricanonical line bundle has nonzero sections, then it induces the pluricanonical maps£p . It's very interesting to know when the pluricanonical maps give "Iitaka fibrations". The answer is well-known for curves and surfaces. For higher dimensional varieties of general type, Kollar gave a exponential bound in dimension for m such that£p defines the Iitaka fibration under some mild condition. We show that if the varieties is of maximal Albanese dimension and defined over complex number C, then a linear bound is enough. We would like to remark that a similar result holds for varieties not necessarily of general type. |