# Manifolds covered by lines and extremal rays - Mathematics > Algebraic Geometry

Abstract: Let $X$ be a smooth complex projective variety and let $H \in \picX$ be anample line bundle. Assume that $X$ is covered by rational curves with degreeone 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 whosenumerical class spans an extremal ray in the cone of curves $\coneX$.

Author: Carla Novelli, Gianluca Occhetta

Source: https://arxiv.org/