Varietes faiblement speciales a courbes entieres degenerees

Details Varietes faiblement speciales a courbes entieres degenerees Varietes faiblement speciales a courbes entieres degenerees

2005-12-06

arxiv.org/abs/math/0512124v4

Mathematics

Algebraic Geometry

17 pages, second version corrects some typographical errors and provide some details concerning the last part of the proof

Scientific paper

We show that certain non-special but weakly special threefolds $X$ constructed by Bogomolov-Tschinkel enjoy strong complex hyperbolicity properties: their entire curves are algebraically degenerate and lie either on a fixed divisor or on the fiber of the unique elliptic fibration on $X$. These properties are consistent with the conjectural link between hyperbolicity and arithmetics of projective manifolds. The arithmetic counterpart of this hyperbolicity property (the non-potential density of $X$, object of two conflicting conjectures) remains however open.

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