Ampleness of canonical divisors of hyperbolic normal projective varieties
Algebraic Geometry
2019-07-08 v1 Complex Variables
Differential Geometry
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.
Keywords
Cite
@article{arxiv.1407.5694,
title = {Ampleness of canonical divisors of hyperbolic normal projective varieties},
author = {Fei Hu and Sheng Meng and De-Qi Zhang},
journal= {arXiv preprint arXiv:1407.5694},
year = {2019}
}
Comments
Mathematische Zeitschrift (to appear)