Picard numbers in a family of hyperk\"ahler manifolds - A supplement to   the article of R. Borcherds, L. Katzarkov, T. Pantev, N. I. Shepherd-Barron
  We remark the density of the jumping loci of the Picard number of a hyperk\"ahler manifold under small one-dimensional deformation and provide some applications for the Mordell-Weil groups of Jacobian K3 surfaces. 
Keiji Oguiso