Normal bundles of rational curves on complete intersections
Normal bundles of rational curves on complete intersections
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完全交点上有理曲线的法向丛
DOI：
10.1142/s0219199718500116
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发表时间：
2017
影响因子：
1.6
通讯作者：
Eric Riedl
中科院分区：
文献类型：
--
作者：
Izzet Coskun;Eric Riedl
设[Formula：see text]是[Formula：see text]类型的一般Fano完全交集。如果至少有一个[公式：当[Formula：see text]大于[Formula：see text]时，我们证明了[Formula：see text]包含次数为[Formula：see text]的有理曲线，其法丛是平衡的。如果所有[公式：见正文]为[公式：见正文]和[公式：我们证明了[Formula：see text]包含具有平衡法丛的次数[Formula：see text]的有理曲线。作为应用，我们证明了田[27]，陈和朱[4]定理的一个更强的版本，即[公式：见正文]通过在最优次数的[公式：见正文]中显示非常自由的有理曲线而可分离地有理连通。
Let [Formula: see text] be a general Fano complete intersection of type [Formula: see text]. If at least one [Formula: see text] is greater than [Formula: see text], we show that [Formula: see text] contains rational curves of degree [Formula: see text] with balanced normal bundle. If all [Formula: see text] are [Formula: see text] and [Formula: see text], we show that [Formula: see text] contains rational curves of degree [Formula: see text] with balanced normal bundle. As an application, we prove a stronger version of the theorem of Tian [27], Chen and Zhu [4] that [Formula: see text] is separably rationally connected by exhibiting very free rational curves in [Formula: see text] of optimal degrees.