Hyperbolicity of bases for maximally variational families of smooth projective varieties

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.