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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.

The Automorphism Group of the Hilbert Scheme of Two Points on a Generic Projective K3 Surface