• Corpus ID: 243861040

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

  title={Algebraic fibre spaces with strictly nef relative anti-log canonical divisor},
  author={Jie Liu and Wenhao Ou and Juanyong Wang and Xiaokui Yang and Guolei Zhong},
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 fibration with rationally connected fibres, and the base Y is a canonically polarized hyperbolic projective manifold. In particular, whenY is a single point, we establish thatX is rationally connected. Moreover, when dimX = 3 and −(KX + ) is strictly nef, we prove that −(KX + ) is ample, which… 

Strictly nef divisors on singular threefolds

Let X be a normal projective variety with only klt singularities, and LX a strictly nef Q-divisor on X. In this paper, we study the singular version of Serrano’s conjecture, i.e., the ampleness



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

The pseudo-effective cone of a compact K\

We prove that a holomorphic line bundle on a projective manifold is pseudo-effective if and only if its degree on any member of a covering family of curves is non-negative. This is a consequence of a

On the canonical threefolds with strictly nef anticanonical divisors

Any ample Cartier divisor D on a projective variety X is strictly nef (i.e. D.C>0 for any effective curve C on X). In general, the converse statement does not hold. But this is conjectured to be true

On fundamental groups of algebraic varieties and value distribution theory

— If a smooth projective variety X admits a non-degenerate holomorphic map C → X from the complex plane C, then for any finite dimensional linear representation of the fundamental group of X the

Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities

In this article we study the structure of klt projective varieties with nef anticanonical divisor (and more generally, varieties of semi-Fano type), especially the canonical fibrations associated to

On projective varieties with strictly nef tangent bundles

On foliations with nef anti-canonical bundle

In this paper we prove that the anti-canonical bundle of a holomorphic foliation $\mathcal{F}$ on a complex projective manifold cannot be nef and big if either $\mathcal{F}$ is regular, or

A decomposition theorem for projective manifolds with nef anticanonical bundle

Let X X be a simply connected projective manifold with nef anticanonical bundle. We prove that X X is a product of a rationally connected manifold and a manifold with trivial

Strictly nef divisors and Fano threefolds.

We are working in the category of projective varieties defined over the field of complex numbers. This paper is devoted to the study of Cartier divisors whose intersection product with every curve is

Special Varieties and classification Theory

A new class of compact K\"ahler manifolds, called special, is defined, which are the ones having no surjective meromorphic map to an orbifold of general type. The special manifolds are in many