The exceptional set and the Green-Griffiths locus do not always coincide

Abstract

We give a very simple criterion in order to ensure that the Green-Griffiths locus of a projective manifold is the whole manifold. Next, we use it to show that the Green-Griffiths locus of any projective manifold uniformized by a bounded symmetric domain of rank greater than one is the whole manifold. In particular, this clarifies an old example given by M. Green to S. Lang.

This is a completely renewed version which strictly contains our previous version 1. We now deal with arbitrary bounded symmetric domains and consider also some arithmetic aspects. 27 pages, no figures, comments are welcome