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
Abstract
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.
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