A remark on the codimension of the Green–Griffiths locus of generic projective hypersurfaces of high degree

We show that for every smooth generic projective hypersurface , there exists a proper subvariety such that codim X Y ≧ 2 and for every non constant holomorphic entire map ƒ : ℂ → X one has ƒ (ℂ) ⊂ Y , provided deg X ≧ 2 n 5 . In particular, we obtain an effective confirmation of the Kobayashi conjecture for threefolds in .