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1 results

  • On existence of log minimal models

  • Part of
  • Caucher Birkar
  • Journal:
    Compositio Mathematica / Volume 146 / Issue 4 / July 2010
    Published online by Cambridge University Press:
    05 February 2010, pp. 919-928
    Print publication:
    July 2010
    • Article
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  • In this paper, we prove that the log minimal model program in dimension d−1 implies the existence of log minimal models for effective lc pairs (e.g. of non-negative Kodaira dimension) in dimension d. In fact, we prove that the same conclusion follows from a weaker assumption, namely, the log minimal model program with scaling in dimension d−1. This enables us to prove that effective lc pairs in dimension five have log minimal models. We also give new proofs of the existence of log minimal models for effective lc pairs in dimension four and of the Shokurov reduction theorem.