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

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

2008-10-27

arxiv.org/abs/0810.4911v1

Mathematics

Algebraic Geometry

31 pages

Scientific paper

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 $d\geq 93.$

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