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arXiv · 0805.2069

Manifolds covered by lines and extremal rays

Carla Novelli·Gianluca Occhetta
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Abstract

Let $X$ be a smooth complex projective variety and let $H \in \pic(X)$ 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 $(\dim X -1)/2$. We prove that there is a covering family of such curves whose numerical class spans an extremal ray in the cone of curves $\cone(X)$.

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Carla Novelli, Gianluca Occhetta. 2008-05-14. Manifolds covered by lines and extremal rays. https://doi.org/10.4153/cmb-2011-119-7

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