On the length of an extremal rational curve. (English) Zbl 0751.14007

It is proved that the exceptional locus of an elementary contraction of an algebraic variety is covered by rational curves whose degrees with respect to the canonical divisor \(K\) are bounded by twice the dimension. The theorem is formulated in the log category so that it applies, e.g., to the case in which \(K\) is relatively trivial. In the course of the proof, a subadjunction formula is proved using a vanishing theorem of Kodaira type.
Reviewer: Y.Kawamata (Tokyo)


14E30 Minimal model program (Mori theory, extremal rays)
14H99 Curves in algebraic geometry
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