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Manifolds Covered by Lines and Extremal Rays

Published online by Cambridge University Press:  20 November 2018

Carla Novelli  and
Gianluca Occhetta
Carla Novelli
Affiliation:
Dipartimento di Matematica “F. Casorati”, Università di Pavia, via Ferrata 1, I-27100 PaviaandDipartimento di Matematica Pura e Applicata, Università di Padova, via Trieste 63, I-35121, Padova, Italye-mail: novelli@math.unipd.it
Gianluca Occhetta
Affiliation:
Dipartimento di Matematica, Università di Trento, via Sommarive 14, I-38123 Povo (TN), Italye-mail: gianluca.occhetta@unitn.it
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Abstract

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Let $X$ be a smooth complex projective variety, and let $H\,\in \,\text{Pic}\left( X \right)$ 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 $\left( \dim\,X\,-\,1 \right)/2$. We prove that there is a covering family of such curves whose numerical class spans an extremal ray in the cone of curves $\text{NE}\left( X \right)$.

Keywords

14J4014E3014C99rational curvesextremal rays
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 4 , 01 December 2012 , pp. 799 - 814
Copyright
Copyright © Canadian Mathematical Society 2012

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