Ya Deng (IHES)Plus d'infos...Lieu : Salle 3L8 Résumé : For maximally varying, smooth fibrations of polarized manifolds with semi-ample canonical bundle, the Shafarevich-Viehweg conjecture says that the base spaces of these fibrations should be of log general type. This deep conjecture was proved by Campana-Paun in 2015. In this talk I will show that these base spaces are furthermore pseudo Kobayashi hyperbolic, i.e. Kobayashi hyperbolic modulo a proper Zariski closed subset, as predicted by the famous Lang conjecture. As a consequence, this in particular proves a conjecture by Viehweg-Zuo in 2003 : moduli spaces of polarized manifolds with semi-ample canonical bundle are Brody hyperbolic (containing no entire curves). I will also present another related work (jointly with Dan Abramovich) on the Kobayashi hyperbolicity for moduli spaces of general type manifolds. 
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