Abstract
The Green-Griffiths-Lang conjecture stipulates that for every projective variety X of general type over \({\mathbb C}\), there exists a proper algebraic subvariety of X containing all non constant entire curves \(f:{\mathbb C}\rightarrow X\). 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 \(T_X\). We then give a sufficient criterion for the Kobayashi hyperbolicity of an arbitrary directed variety (X, V).
In memory of M. Salah Baouendi
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Demailly, JP. (2015). Towards the Green-Griffiths-Lang Conjecture. In: Baklouti, A., El Kacimi, A., Kallel, S., Mir, N. (eds) Analysis and Geometry. Springer Proceedings in Mathematics & Statistics, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-319-17443-3_8
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