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

@inproceedings{Liu2021AlgebraicFS, 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}, year={2021} }

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…

## One Citation

### Strictly nef divisors on singular threefolds

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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…

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