Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of ???? points on a generic projective ????3 surface ????, for any ???? ≥ 2. We show that Aut(????[????]) is either trivial or generatedby a non-symplectic involution and we determine numerical and divisorial conditionswhich allow us to distinguish between the two cases. As an application of these results we prove that, for any ???? ≥ 2, there exist infinitely many admissible degrees for thepolarization of the ????3 surface ???? such that ????[????] admits a non-natural involution. This provides a generalization of the results of [7] for ???? = 2