Joel Merker, Ecole Normale Supérieure, Paris

On the Green-Griffiths Conjecture

 

Abstract

In 1979, Green and Griffiths conjectured that in every projective algebraic variety X of general type, there exists a certain proper subvariety Y with the property that every nonconstant entire holomorphic curve f : C ® X landing in X must in fact lie inside Y. For projective hypersurfaces X, Siu showed in 2004 that there is an integer dn such that every generic hypersurface X in Pn+1(C) of degree d ³dn, such an Y exists. The talk, based on the bundle of invariant jet differentials and on a new construction of explicit slanted vector fields tangent to the space of vertical jets to the universal hypersurface (realizing an idea of Siu), will present a recent complete detailed proof of such a kind of algebraic degeneracy statement, with the effective degree bound :

 

improving the double exponential bound announced (joint with S. Diverio and E. Rousseau) on arxiv.org in November 2008.