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arXiv · 1412.2986

Towards the Green-Griffiths-Lang conjecture

Jean-Pierre Demailly
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Abstract

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 hyperbolicity of an arbitrary directed variety (X,V). This work is dedicated to the memory of Professor Salah Baouendi.

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BibTeXRIS

Jean-Pierre Demailly. 2015-04-09. Towards the Green-Griffiths-Lang conjecture. https://arxiv.org/abs/1412.2986

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