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arXiv · 1407.5694

Ampleness of canonical divisors of hyperbolic normal projective varieties

Fei Hu·Sheng Meng·De-Qi Zhang
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Abstract

Let X be a projective variety which is algebraic Lang hyperbolic. We show that Lang's conjecture holds (one direction only): X and all its subvarieties are of general type and the canonical divisor K_X is ample at smooth points and Kawamata log terminal points of X, provided that K_X is Q-Cartier, no Calabi-Yau variety is algebraic Lang hyperbolic and a weak abundance conjecture holds.

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Fei Hu, Sheng Meng, De-Qi Zhang. 2014-07-21. Ampleness of canonical divisors of hyperbolic normal projective varieties. https://doi.org/10.1007/s00209-014-1351-1

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