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

Gianluca Pacienza (1) , Erwan Rousseau (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Motivated by the Green-Griffiths conjecture, we study maximal rank holomorphic maps from $\C^p$ 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 maximal rank holomorphic maps from $\C^2$ into the very general degree $d$ hypersurface in $\bP^4$, as soon as $d\geq 93.$

Mots clés: hyperbolicity of projective varieties; holomorphic mappings; jet bundles; Green-Griffiths conjecture; Kobayashi conjecture

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Gianluca Pacienza, Erwan Rousseau. Generalized Demailly-Semple jet bundles and holomorphic mappings into complex manifolds. 2008. ⟨hal-00334768⟩