Vortrag von Dr. Ya Deng
Sprecher eingeladen von: Prof. Dr. Joseph Ayoub
Datum: 29.11.21 Zeit: 13.15 - 15.00 Raum: Y27H25
Proven by A. Parshin and S. Arakelov in 70's, Shafarevich's hyperbolicity conjecture states that a smooth family of curves of genus at least 2 parametrized by a non hyperbolic curve has to be isotrivial: all the ﬁbres are isomorphic. A complex quasi-projective variety is called pseudo Brody hyperbolic if it does not admit any Zariski dense entire curve. Inspired by Shafarevich's hyperbolicity conjecture, in 2002 Viehweg-Zuo conjectured that if a family of smooth projective varieties with semiample canonical bundle over a quasi-projective variety has maximal variation, then the base is pseudo Brody hyperbolic. In this talk I will explain my recent work on the proof of this conjecture by Viehweg-Zuo, as well as some generalizations.