A Canonical Bundle Formula

  title={A Canonical Bundle Formula},
  author={Osamu Fujino and Shigefumi Mori},
A higher dimensional analogue of Kodaira's canonical bundle formula is obtained. As applications, we prove that the logcanonical ring of a klt pair with 3 is nitely generated, and that there exists an e ectively computable natural numberM such that jMK X j induces the Iitaka bering for every algebraic threefold X with Kodaira dimension = 1. 
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