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A remark on elementary contractions

Published online by Cambridge University Press:  24 October 2008

Qi Zhang
Qi Zhang
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
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Extract

Let X be a smooth projective variety of dimension n over the field of complex numbers. We denote by Kx the canonical bundle of X. By Mori's theory, if Kx is not numerically effective (i.e. if there exists a curve on X which has negative intersection number with Kx), then there exists an extremal ray ℝ+[C] on X and an elementary contraction fR: X → Y associated with ℝ+[C].fR is called a small contraction if it is bi-rational and an isomorphism in co-dimension one.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 1 , July 1995 , pp. 183 - 188
Copyright
Copyright © Cambridge Philosophical Society 1995

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