Cone Theorem Revisited

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


The purpose of this chapter is to present Mori’s original idea (cf. Mori [1][2]) to prove the cone theorem (in the smooth case) through his ingenious method of “bend and break” to produce rational curves of some bounded degree (with respect to an ample divisor or to the canonical divisor). This method leads to the result of Miyaoka—Mori [1] claiming the uniruledness of Mori fiber spaces, yielding the generalization by Kawamata [13] claiming that (every irreducible component of) the exceptional locus of an extremal contraction is also uniruled in general.


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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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