CRM: Centro De Giorgi
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KAWA - Komplex Analysis Workshop VI, 2015

On the Green-Griffiths-Lang and Kobayashi conjectures for the hyperbolicity of algebraic Varieties

speaker: Jean-Pierre Demailly (Université de Grenoble I Institut Fourier, Laboratoire de Mathématiques)

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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