Contraction Theorem

  • Kenji Matsuki
Part of the Universitext book series (UTX)


This chapter starts with characterizing in Section 8-1 the extremal contractions the key geometric operations in the process of the minimal model program, as what we call the contractions of extremal rays described in terms of the convex geometry of the cone of curves, thanks to the cone theorem of Chapter 7. Their existence is guaranteed by the base point freeness theorem of Chapter 6.


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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Kenji Matsuki
    • 1
  1. 1.Department of Mathematics, 1395 Mathematical Science BuildingPurdue UniversityWest LafayetteUSA

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