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arXiv · 1605.04680

Extremal rays and nefness of tangent bundles

Akihiro Kanemitsu
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Abstract

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.

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Akihiro Kanemitsu. 2016-05-16. Extremal rays and nefness of tangent bundles. https://arxiv.org/abs/1605.04680

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