Holomorphic morse inequalities and the Green-Griffiths-Lang conjecture

Abstract

The goal of this work is to study the existence and properties of non entire curves f: ℂ → X 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 prove a significant step of a generalized version of the Green-Griffths-Lang conjecture on the algebraic degeneracy of entire curves.