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}
}
<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… 
View PDF on arXiv
14 Citations
Highly Influential Citations
1
Background Citations
1
Methods Citations
1
Results Citations
1

14 Citations

Almost nef regular foliations and Fujita's decomposition of reflexive sheaves

In this paper, we study almost nef regular foliations. We give a structure theorem of a smooth projective variety $X$ with an almost nef regular foliation $\mathcal{F}$: $X$ admits a smooth morphism…

Algebraic fibre spaces with strictly nef relative anti-log canonical divisor

Let (X, ) be a projective klt pair, and f ∶ X → Y a fibration to a smooth projective variety Y with strictly nef relative anti-log canonical divisor −(KX∕Y + ). We prove that f is a locally constant…

NORMALISED TANGENT BUNDLE, VARIETIES WITH SMALL CODEGREE AND PSEUDOEFFECTIVE THRESHOLD

  • Baohua FuJie Liu
  • Mathematics
    Journal of the Institute of Mathematics of Jussieu
  • 2022
We propose a conjectural list of Fano manifolds of Picard number $1$ with pseudoeffective normalised tangent bundles, which we prove in various situations by relating it to the complete…

Compact K\"ahler manifolds with quasi-positive second Chern-Ricci curvature.

Let $X$ be a compact Kahler manifold. We prove that if $X$ admits a smooth Hermitian metric $\omega$ with quasi-positive second Chern-Ricci curvature $\mathrm{Ric}^{(2)}(\omega)$, then $X$ is…

Strictly nef vector bundles and characterizations of $\mathbb{P}^n$

In this note, we give a brief exposition on the differences and similarities between strictly nef and ample vector bundles, with particular focus on the circle of problems surrounding the geometry of…

Strongly Pseudo-Effective and Numerically Flat Reflexive Sheaves

  • Xiaojun Wu
  • Mathematics
    The Journal of Geometric Analysis
  • 2022
In this paper, we discuss the concept of strongly pseudo-effective vector bundle and also introduce strongly pseudo-effective torsion-free sheaves over compact Kähler manifolds. We show that a…

Projectively flat klt varieties

In the context of uniformisation problems, we study projective varieties with klt singularities whose cotangent sheaf admits a projectively flat structure over the smooth locus. Generalising work of…

Pseudo-effective and numerically flat reflexive sheaves

In this note, we discuss the concept of pseudoeffective vector bundle and also introduce pseudoeffective torsion-free sheaves over compact Kahler manifolds. We show that a pseudoeffective reflexive…

Strictly nef vector bundles and characterizations of ℙn

Abstract In this note, we give a brief exposition on the differences and similarities between strictly nef and ample vector bundles, with particular focus on the circle of problems surrounding the…

Abundance theorem for minimal compact K\"ahler manifolds with vanishing second Chern class

  • 2022

References

SHOWING 1-10 OF 85 REFERENCES

Semistability and Restrictions of tangent bundle to curves

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…

Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties

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 $X$…

On projective varieties with strictly nef tangent bundles

Semistable sheaves on projective varieties and their restriction to curves

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…

Projective manifolds whose tangent bundles are numerically effective

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…

Restriction of stable sheaves and representations of the fundamental group

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,…

On codimension 1 del Pezzo foliations on varieties with mild singularities

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…

On Polarized Manifolds Whose Adjoint Bundles Are Not Semipositive

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…

PSEUDO-EFFECTIVE LINE BUNDLES ON COMPACT KÄHLER MANIFOLDS

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…

CHARACTERIZATION OF PROJECTIVE SPACES AND $\mathbb{P}^{r}$ -BUNDLES AS AMPLE DIVISORS

  • 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…
...