Generalized Demailly–Semple jet bundles and holomorphic mappings into complex manifolds

AbstractMotivated by the Green–Griffiths conjecture, we study (non-constant) maximal rank holomorphic maps from Cp into complex manifolds. When p>1 such maps should in principle be more tractable than entire curves. We extend to this setting the jet-bundles techniques introduced by Semple, Green–Griffiths and Demailly. Our main application is the non-existence of (non-constant) maximal rank holomorphic maps from C2 into the very general degree d hypersurface in P4, as soon as d⩾93