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Manifolds Covered by Lines and Extremal Rays
Published online by Cambridge University Press: 20 November 2018
Abstract
Let $X$ be a smooth complex projective variety, and let $H\,\in \,\text{Pic}\left( X \right)$ be an ample line bundle. Assume that $X$ is covered by rational curves with degree one with respect to $H$ and with anticanonical degree greater than or equal to $\left( \dim\,X\,-\,1 \right)/2$. We prove that there is a covering family of such curves whose numerical class spans an extremal ray in the cone of curves $\text{NE}\left( X \right)$.
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- Copyright © Canadian Mathematical Society 2012
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