The automorphism group of the Hilbert scheme of two points on a generic   projective K3 surface
  We determine the automorphism group of the Hilbert scheme of two points on a generic projective K3 surface of any polarization. We obtain in particular new examples of Hilbert schemes of points having non-natural non-symplectic automorphisms. The existence of these automorphisms depends on solutions of Pell's equation. 
Samuel Boissi\`ere, Andrea Cattaneo, Marc Nieper-Wisskirchen and   Alessandra Sarti
math.AG