2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79408We show the density of the jumping loci of the Picard number of a hyperkähler manifold under small deformation and provide several applications. In particular, we apply this to reveal the structure of hierarchy among all the narrow Mordell-Weil lattices of Jacobian K3 surfaces.16 pages, AMSTeXAlgebraic Geometry14J05, 14J10, 14J28, 14E27text