Modul:   MAT770  Oberseminar: Algebraische Geometrie

On the hyperbolicity of general hypersurfaces

Vortrag von Dr. Damian Brotbek

Sprecher eingeladen von: Prof. Dr. Joseph Ayoub

Datum: 09.10.17  Zeit: 13.15 - 14.45  Raum: Y27H25

A smooth projective variety over the complex numbers is said to be (Brody) hyperbolic if it doesn't contain any entire curve. Kobayashi conjectured in the 70's that general hypersurfaces of sufficiently large degree in P^N are hyperbolic. This conjecture was only proven recently by Siu. The purpose of this talk is to present another proof of this conjecture. The main idea of the proof, based on the theory of jet differential equations, is to establish that a stronger property, open in the Zariski topology, is satisfied for suitable deformations of Fermat type hypersurfaces.