2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60473We remark the density of the jumping loci of the Picard number of a hyperkähler manifold under small one-dimensional deformation and provide some applications for the Mordell-Weil groups of Jacobian K3 surfaces.12 pages, AMS TeXAlgebraic Geometrytext