Uniform families of minimal rational curves on Fano manifolds
Uniform families of minimal rational curves on Fano manifolds
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Fano 流形上最小有理曲线的一致族
DOI：
10.1007/s13163-015-0183-9
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发表时间：
2016
影响因子：
0.8
通讯作者：
Kiwamu
中科院分区：
文献类型：
--
作者：
Occhetta;Gianluca; Sola Conde;Luis E.;Watanabe;Kiwamu
众所周知，Picard数为1的有理齐次流形上的极小有理曲线族是一致的，在这个意义上，流形的切丛在族的每条曲线上具有相同的分裂类型。本文证明了在Picard数为1的Fano流形上的极小有理曲线族的某些强一致性条件允许证明该流形是齐次的。
It is a well known fact that families of minimal rational curves on rational homogeneous manifolds of Picard number one are uniform, in the sense that the tangent bundle to the manifold has the same splitting type on each curve of the family. In this note we prove that certain—stronger—uniformity conditions on a family of minimal rational curves on a Fano manifold of Picard number one allow to prove that the manifold is homogeneous.