Demailly, Jean-Pierre; Matematični kolokvij december 2005

Iz MaFiRaWiki

Algebraic differential equations and hyperbolicity

Jean-Pierre Demailly

Institut Fourier, Université de Grenoble

15. december 2005

The talk will explain a few basic facts about entire holomorphic curves drawn in algebraic manifolds. A projective algebraic manifold is said to be Brody hyperbolic if it does not possess such curves. By a well-known conjecture of Kobayashi, it is expected that a generic hypersurface of high degree in projective space is Brody hyperbolic. In this study, algebraic differential equations play a prominent role. We will explain how they are involved, and will present a few related open problems concerning the structure of the ring of algebraic differential operators on germs of curves in surfaces.

Osebna orodja