The Michigan Mathematical Journal

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 n6 is either a rational homogeneous manifold or the product of n7 copies of P1 and a Fano 7-fold X0 constructed by G. Ottaviani. We also clarify that X0 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
Received: 24 May 2017
Revised: 31 July 2017
First available in Project Euclid: 9 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1549681299

Digital Object Identifier
doi:10.1307/mmj/1549681299

Mathematical Reviews number (MathSciNet)
MR3961218

Zentralblatt MATH identifier
07084764

Subjects
Primary: 14J45: Fano varieties
Secondary: 14J40: $n$-folds ($n > 4$) 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]

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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