Manifolds covered by lines and extremal rays

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 $\cone(X)$.

Major revision, to appear in Canadian Mathematical Bulletin

References in corpus (2)

• The cone of curves of Fano varieties of coindex four
• Projective manifolds containing a large linear subspace with nef normal bundle

Cited by in corpus (1)

• Projective manifolds containing a large linear subspace with nef normal bundle