Manifolds Covered by Lines and Extremal Rays

Novelli, Carla ; Occhetta, Gianluca

Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 799-814

Résumé

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 $\text{NE}\left( X \right)$ .

Détail

DOI : 10.4153/CMB-2011-119-7

Mots-clés : 14J40, 14E30, 14C99, rational curves, extremal rays

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