# Projective manifolds whose tangent bundle contains a strictly nef subsheaf

@article{Liu2020ProjectiveMW,
title={Projective manifolds whose tangent bundle contains a strictly nef subsheaf},
author={Jie Liu and Wenhao Ou and Xiaokui Yang},
journal={Journal of Algebraic Geometry},
year={2020}
}
• Published 18 April 2020
• Computer Science
• Journal of Algebraic Geometry
<p>Suppose that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a projective manifold whose tangent bundle <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T Subscript upper X"> <mml:semantics…
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## References

SHOWING 1-10 OF 85 REFERENCES

AbstractWe consider all complex projective manifolds X that satisfy at least one of the following three conditions: (1)There exists a pair $${(C\,,\varphi)}$$ , where C is a compact connected
• Mathematics
• 2016
Given a quasi-projective variety X with only Kawamata log terminal singularities, we study the obstructions to extending finite \'etale covers from the smooth locus $X_{\mathrm{reg}}$ of $X$ to $X$
• Mathematics
Journal de Mathématiques Pures et Appliquées
• 2019
• Mathematics
• 1982
Let X be a nonsingular projective variety of dimension n over an algebraically closed field k. Let H be a very ample line bundle on X. If V is a torsion free coherent sheaf on X we define deg V to be
• Mathematics
• 1991
In 1979, Mori [Mo] proved the so-called Hartshorne-Frankel conjecture: Every projective n-dimensional manifold with ample tangent bundle is isomorphic to the complex projective space P,. A
• Mathematics
• 1984
Let X be a projective smooth variety of dimension n over an algebraically closed field k. Let H be an ample line bundle on X. A torsion free sheaf V on X is said to be stable (respectively,
• Mathematics
• 2012
In this paper we extend to the singular setting the theory of Fano foliations developed in our previous paper (Araujo and Druel, Adv Math 238:70–118, 2013). A $$\mathbb {Q}$$Q-Fano foliation on a
Let L be an ample (not necessarily very ample) line bundle On a projective variety M with dim M = n having only rational normal Gorensteib. singularities. Let m be the dualizing sheaf and let K be
• Mathematics
• 2000
The goal of this work is to pursue the study of pseudo-effective line bundles and vector bundles. Our first result is a generalization of the Hard Lefschetz theorem for cohomology with values in a
• Jie Liu
• Mathematics
Nagoya Mathematical Journal
• 2017
Let $X$ be a projective manifold of dimension $n$ . Suppose that $T_{X}$ contains an ample subsheaf. We show that $X$ is isomorphic to $\mathbb{P}^{n}$ . As an application, we derive the