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June 2019 Extremal Rays and Nefness of Tangent Bundles
Akihiro Kanemitsu
Michigan Math. J. 68(2): 301-322 (June 2019). DOI: 10.1307/mmj/1549681299

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.

Citation

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Akihiro Kanemitsu. "Extremal Rays and Nefness of Tangent Bundles." Michigan Math. J. 68 (2) 301 - 322, June 2019. https://doi.org/10.1307/mmj/1549681299

Information

Received: 24 May 2017; Revised: 31 July 2017; Published: June 2019
First available in Project Euclid: 9 February 2019

zbMATH: 07084764
MathSciNet: MR3961218
Digital Object Identifier: 10.1307/mmj/1549681299

Subjects:
Primary: 14J45
Secondary: 14J40, 14M17

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 2 • June 2019
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