Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture

Jean-Pierre Demailly (1)

1 IF - Institut Fourier

The goal of this work is to study the existence and properties of non constant entire curves f drawn in a complex irreducible n-dimensional variety X, and more specifically to show that they must satisfy certain global algebraic or differential equations as soon as X is projective of general type. By means of holomorphic Morse inequalities and a probabilistic analysis of the cohomology of jet spaces, we are able to reach a significant step towards a generalized version of the Green-Griffiths-Lang conjecture.

Mots clés: Chern curvature; Holomorphic Morse inequality; Jet bundle; Cohomology group; Entire curve; Algebraic degeneration; Weighted projective space; Green-Griffiths-Lang conjecture

Domaines: Géométrie algébrique [math.AG]

Jean-Pierre Demailly. Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture. 2010. ⟨hal-00536319v2⟩