# Effective Iitaka fibrations

Eckart Viehweg, De-Qi Zhang

Number | 12 |
---|---|

Author | Eckart Viehweg |

Year | 2007 |

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,B_{n−2}), where b > 0 is minimal with |bK_{F}| ≠ ∅ for a general fibre F of an Iitaka fibration of X, and where B_{n−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.