Picard number of the generic fiber of an abelian fibered hyperkaehler manifold
Abstract
Description
We shall show that the Picard number of the generic fiber, in the sense of scheme, of an abelian fibered hyperkähler manifold over the projective space is always one. We then give a few applications for the Mordell-Weil group. In particular, by deforming O'Grady's 10-dimensional manifold, we construct an abelian fibered hyperkähler manifold of Mordell-Weil rank 20, which is the maximum possible among all known ones.
Corrected, final version. to appear in Math. Annalen
Corrected, final version. to appear in Math. Annalen