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Manifolds Covered by Lines and Extremal Rays

 Printed: Dec 2012
  • Carla Novelli,
    Dipartimento di Matematica ``F. Casorati'', UniversitĂ  di Pavia, via Ferrata 1, I-27100 Pavia
  • Gianluca Occhetta,
    Dipartimento di Matematica, UniversitĂ  di Trento, via Sommarive 14, I-38123 Povo (TN), Italy
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Let $X$ be a smooth complex projective variety, and let $H \in \operatorname{Pic}(X)$ 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 $\operatorname{NE}(X)$.
Keywords: rational curves, extremal rays rational curves, extremal rays
MSC Classifications: 14J40, 14E30, 14C99 show english descriptions $n$-folds ($n>4$)
Minimal model program (Mori theory, extremal rays)
None of the above, but in this section
14J40 - $n$-folds ($n>4$)
14E30 - Minimal model program (Mori theory, extremal rays)
14C99 - None of the above, but in this section

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