Geodesic
Manifolds Covered by Lines and Extremal Rays
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 799-814

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DOI

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 $\text{NE}\left( X \right)$ .
DOI : 10.4153/CMB-2011-119-7
Mots-clés : 14J40, 14E30, 14C99, rational curves, extremal rays 
Novelli, Carla; Occhetta, Gianluca. Manifolds Covered by Lines and Extremal Rays. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 799-814. doi: 10.4153/CMB-2011-119-7
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     title = {Manifolds {Covered} by {Lines} and {Extremal} {Rays}},
     journal = {Canadian mathematical bulletin},
     pages = {799--814},
     year = {2012},
     volume = {55},
     number = {4},
     doi = {10.4153/CMB-2011-119-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-119-7/}
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