Higher dimensional tautological inequalities and applications
arXiv:1006.5138
Abstract
We study the degeneracy of holomorphic mappings tangent to holomorphic foliations on projective manifolds. Using Ahlfors currents in higher dimension, we obtain several strong degeneracy statements.
28 pages; v2: algebraic degeneracy in the strong sense is obtained in several statements. We state a generalized Green-Griffiths-Lang conjecture and study it in dimension 3