Abstract view
Manifolds Covered by Lines and Extremal Rays


Published:20110614
Printed: Dec 2012
Carla Novelli,
Dipartimento di Matematica ``F. Casorati'', UniversitĂ di Pavia, via Ferrata 1, I27100 Pavia
Gianluca Occhetta,
Dipartimento di Matematica, UniversitĂ di Trento, via Sommarive 14, I38123 Povo (TN), Italy
Abstract
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 $\operatorname{NE}(X)$.