2008/03/08 by Keiji Oguiso, Oguiso, Keiji
Mathematics · #14D06 #14J28 #14J40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #math.AG #msc:14D06 #msc:14J28 #msc:14J40
paper · pdf · doi:10.48550/arxiv.0803.1205
Corrected, final version. to appear in Math. Annalen
openalex publication_date 2008/03/08 · arxiv created 2009/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.