6 novembre 2019

Ya Deng (IHES)
Hyperbolicity of moduli spaces of high dimensional manifolds

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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.

Hyperbolicity of moduli spaces of high dimensional manifolds  Version PDF