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. |