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

2018/01/17 by Alberto Cattaneo, Cattaneo, Alberto · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1801.05682

Abstract

We study automorphisms of the Hilbert scheme of n points on a generic\nprojective K3 surface S, for any n \≥ 2. We show that the automorphism\ngroup of S^[n] is either trivial or generated by a non-symplectic\ninvolution and we determine numerical and divisorial conditions which allow us\nto distinguish between the two cases. As an application of these results we\nprove that, for any n \≥ 2, there exist infinite values for the degree of\nS such that S^[n] admits a non-natural involution. This provides a\ngeneralization of results by Boissi `ere--Cattaneo--Nieper-Wisskirchen--Sarti\nfor n=2.\n

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