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1 results

  • Reduction maps and minimal model theory

  • Part of
  • Yoshinori Gongyo, Brian Lehmann
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 2 / February 2013
    Published online by Cambridge University Press:
    04 December 2012, pp. 295-308
    Print publication:
    February 2013
    • Article
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  • We use reduction maps to study the minimal model program. Our main result is that the existence of a good minimal model for a Kawamata log terminal pair (X,Δ) can be detected on a birational model of the base of the (KX+Δ)-trivial reduction map. We then interpret the main conjectures of the minimal model program as a natural statement about the existence of curves on X.