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

Alberto Cattaneo

Mathematische Nachrichten, 2019, vol. 292, issue 10, 2137-2152

Abstract: We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any n≥2. We show that Aut(S[n]) is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any n≥2, there exist infinitely many admissible degrees for the polarization of the K3 surface S such that S[n] admits a non‐natural involution. This provides a generalization of the results of [7] for n=2.

Date: 2019
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