We give a very simple criterion for the Green–Griffiths locus of a projective manifold to be the whole manifold. Then, 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 undetailed example given by M. Green to S. Lang.
Cite this article
Simone Diverio, Erwan Rousseau, The exceptional set and the Green–Griffiths locus do not always coincide. Enseign. Math. 61 (2015), no. 3/4, pp. 417–452DOI 10.4171/LEM/61-3/4-6