Manifolds covered by lines and extremal rays

Details Manifolds covered by lines and extremal rays Manifolds covered by lines and extremal rays

2008-05-14

arxiv.org/abs/0805.2069v2

Mathematics

Algebraic Geometry

Major revision, to appear in Canadian Mathematical Bulletin

Scientific paper

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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