The Michigan Mathematical Journal
- Michigan Math. J.
- Volume 68, Issue 2 (2019), 301-322.
Extremal Rays and Nefness of Tangent Bundles
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 -fold with the same condition and Picard number greater than is either a rational homogeneous manifold or the product of copies of and a Fano -fold constructed by G. Ottaviani. We also clarify that has a non-nef tangent bundle and in particular is not rational homogeneous.
Michigan Math. J., Volume 68, Issue 2 (2019), 301-322.
Received: 24 May 2017
Revised: 31 July 2017
First available in Project Euclid: 9 February 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14J45: Fano varieties
Secondary: 14J40: $n$-folds ($n > 4$) 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
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