Manifolds Covered by Lines and Extremal Rays

Canadian mathematical bulletin

Gianluca Occhetta¹  Carla Novelli² 

[1] Dipartimento di Matematica, Università di Trento, via Sommarive 14, I-38123 Povo (TN), Italy;Dipartimento di Matematica ``F. Casorati', Università di Pavia, via Ferrata 1, I-27100 Pavia

关键词: rational curves;    extremal rays;   

DOI  :  10.4153/CMB-2011-119-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $X$ be a smooth complex projective variety, and let $H inoperatorname{Pic}(X)$be an ample line bundle. Assume that $X$ is covered by rationalcurves with degree one with respect to $H$ and with anticanonicaldegree greater than or equal to $(dim X -1)/2$. We prove that thereis a covering family of such curves whose numerical class spans anextremal ray in the cone of curves $operatorname{NE}(X)$.

【 授权许可】

Unknown