# Towards the Green-Griffiths-Lang conjecture

@article{Demailly2014TowardsTG,
title={Towards the Green-Griffiths-Lang conjecture},
author={J Demailly},
journal={arXiv: Algebraic Geometry},
year={2014}
}
• J. Demailly
• Published 9 December 2014
• Mathematics
• arXiv: Algebraic Geometry
The Green-Griffiths-Lang conjecture stipulates that for every projective variety X of general type over C, there exists a proper algebraic subvariety of X containing all non constant entire curves f : C $\rightarrow$ X. Using the formalism of directed varieties, we prove here that this assertion holds true in case X satisfies a strong general type condition that is related to a certain jet-semistability property of the tangent bundle TX . We then give a sufficient criterion for the Kobayashi…
Recent results on the Kobayashi and Green-Griffiths-Lang conjectures
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