Orateur(s)  Ya Deng  Université de Strasbourg,

Titre  On the ampleness of the logarithmic jet bundle 
Date  28/11/2017 
Horaire  14:00 à 15:00 

Résume  A complex (not necessarily compact) manifold X is said (Brody) hyperbolic if there exists no nonconstant entire curves 𝑓 ∶ ℂ → X. In the 70s, Kobayashi conjectured that a general hypersurface X of high degree in the projective space ℙ𝑛 is hyperbolic. Moreover, he further conjectured that the complement ℙ𝑛\X should also be hyperbolic. The first conjecture was proved by YumTong Siu and Damian Brotbek independently. In this talk, I will present a recent result on the ampleness of the logarithmic jet bundle of the pair (ℙ𝑛, X); in particular, this gives a proof of the second conjecture by Kobayashi. The techniques are based on the construction of logarithmic jet differentials, which are the obstructions of the entire curves. The talk is based on joint projects with Brotbek. 
Salle  Barre 1525, 5ème étage, salle 02 
Adresse  Campus Pierre et Marie Curie 