**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 \(f:{\mathbb C}\to X\). Using the formalism of
directed varieties, we prove 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 explain how this result can be used to investigate
the long-standing conjecture of Kobayashi (1970), according to which a
very general algebraic hypersurface of dimension \(n\) and degree at
least \(2n+1\) in the complex projective space \({\mathbb P}^{n+1}\) is
hyperbolic.

Thu 26 Mar, 18:00 - 19:30, Aula Dini

Abstract (pdf)

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