Extremal Rays and Nefness of Tangent Bundles
Extremal Rays and Nefness of Tangent Bundles
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DOI：
10.1307/mmj/1549681299
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发表时间：
2016-05
影响因子：
0.9
通讯作者：
Akihiro Kanemitsu
中科院分区：
文献类型：
--
作者：
Akihiro Kanemitsu
In view of Mori theory, rational homogenous manifolds satisfy a recursive condition: every elementary contraction is a rational homogeneous fibration and the image of any elementary contraction also satisfies the same property. In this paper, we show that a smooth Fano $n$-fold with the same condition and Picard number greater than $n-6$ is either a rational homogeneous manifold or the product of $n-7$ copies of $\mathbb{P}^1$ and a Fano $7$-fold $X_0$ constructed by G. Ottaviani. We also clarify that $X_0$ has non-nef tangent bundle and in particular is not rational homogeneous.
