有理三次连通流形I：线覆盖流形
Rationally cubic connected manifolds I: manifolds covered by lines
摘要：
本文研究了n维\ge 2的光滑复射影极化簇（X，H），它允许H次3的有理曲线的控制族V，使得X的两个一般点可以由V参数化的曲线连接，并且使得存在H次1的有理曲线的覆盖族.我们的主要结果是这些流形的Picard数至多为3，并且，如果等式成立，（X，H）在光滑簇上有一个邻接理论涡卷结构.
英文摘要：
In this paper we study smooth complex projective polarized varieties (X,H) of dimension n \ge 2 which admit a dominating family V of rational curves of H-degree 3, such that two general points of X may be joined by a curve parametrized by V, and such that there is a covering family of rational curves of H-degree one. Our main result is that the Picard number of these manifolds is at most three, and that, if equality holds, (X,H) has an adjuction theoretic scroll structure over a smooth variety.
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