Varietes faiblement speciales a courbes entieres degenerees
Abstract
Description
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.
17 pages, second version corrects some typographical errors and provide some details concerning the last part of the proof
17 pages, second version corrects some typographical errors and provide some details concerning the last part of the proof