On birational transformations of Hilbert schemes of points on K3 surfaces

Abstract

We classify the group of birational automorphisms of Hilbert schemes of points on algebraic K3 surfaces of Picard rank one. We study whether these automorphisms are symplectic or non-symplectic and if there exists a hyperkähler birational model on which they become biregular. We also present new geometrical constructions of these automorphisms.

arXiv comment18 pages. Exposition improved, review of the theory of Pell's equation moved to appendix. Remark 3.7 added, some minor results removed

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