The Michigan Mathematical Journal

Extremal Rays and Nefness of Tangent Bundles

Akihiro Kanemitsu

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 a non-nef tangent bundle and in particular is not rational homogeneous.

Article information

Source
Michigan Math. J., Volume 68, Issue 2 (2019), 301-322.

Dates
Revised: 31 July 2017
First available in Project Euclid: 9 February 2019

https://projecteuclid.org/euclid.mmj/1549681299

Digital Object Identifier
doi:10.1307/mmj/1549681299

Mathematical Reviews number (MathSciNet)
MR3961218

Zentralblatt MATH identifier
07084764

Citation

Kanemitsu, Akihiro. Extremal Rays and Nefness of Tangent Bundles. Michigan Math. J. 68 (2019), no. 2, 301--322. doi:10.1307/mmj/1549681299. https://projecteuclid.org/euclid.mmj/1549681299

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