Talks on Hyperbolicity

We will have several talks around hyperbolicity of varieties on June 28th and June 29th in Mainz. Here you will find the schedule.

Wednesday June 28th

11:15h-12:15h. Damian Brotbek (Strasbourg)
On the hyperbolicity of general hypersurfaces
Abstract: 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 a new 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.

16h-17h. Erwan Rousseau (Marseille)
Hyperbolicity of some singular spaces

17:30h-18:30h. Simone Diverio (Rome)
Rational curves on fiber spaces whose general fiber is an abelian variety of dimension or codimension one

Thursday June 29th

9:15h-10:15h. Frédéric Campana (Nancy)
Some observations on the Green-Griffiths conjecture for orbifold pairs
Abstract: We shall discuss some of the new difficulties, based on an observation of Darondeau and E. Rousseau, occuring when trying to extend to smooth orbifold pairs of general type the known results about the existence of jet differentials.

10:45h:11:45h. Robert Kucharczyk (Zürich)
Borel hyperbolicity

14h-15h. Lionel Darondeau (Marseille)
Complete intersection varieties with ample cotangent bundles
Abstract: This is joint work with Damian Brotbek. We prove that a smooth projective variety contains many subvarieties with ample cotangent bundle, of each dimension up to half its own dimension. We obtain such subvarieties as certain complete intersections.




Organizer: Ariyan Javanpeykar