Rational curves on hypersurfaces

MICHIGAN MATHEMATICAL JOURNAL（2017）

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摘要

Let (X, D) be a pair where X is a projective variety. We study in detail how the behavior of rational curves on X and the positivity of - (K-x + D) and D influence the behavior of rational curves on D. In particular, we give criteria for uniruledness and rational connectedness of components of D.

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