Effective iitaka fibrations

Abstract

For every n-dimensional projective manifold X of Kodaira dimension 2 we show that & Φ|MKX| is birational to an Iitaka fibration for a computable positive integer M = M(b, Bn-2), where b > 0 is minimal with \bKF| ≠ ∅ for a general fibre F of an Iitaka fibration of X, and where Bn-2 is the Betti number of a smooth model of the canonical ℤ/(b)cover of the (n -2)-fold F. In particular, M is a universal constant if the dimension n < 4.