Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

Manifolds Covered by Lines and Extremal Rays

Published:2011-06-14
Printed: Dec 2012
• Carla Novelli,
Dipartimento di Matematica F. Casorati'', Università di Pavia, via Ferrata 1, I-27100 Pavia
• Gianluca Occhetta,
Dipartimento di Matematica, Università di Trento, via Sommarive 14, I-38123 Povo (TN), Italy
 Format: LaTeX MathJax PDF

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 $\operatorname{NE}(X)$.
 Keywords: rational curves, extremal rays
 MSC Classifications: 14J40 - $n$-folds ($n>4$) 14E30 - Minimal model program (Mori theory, extremal rays) 14C99 - None of the above, but in this section

 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2016 : https://cms.math.ca/