On symplectic automorphisms of hyperk\"ahler fourfolds of K3[2] type

Abstract

The present paper proves that finite symplectic groups of automorphisms of hyperk\"ahler fourfolds deformation equivalent to the Hilbert scheme of two points on a K3 surface are contained in the simple group Co1. Then we give an example of a symplectic automorphism of order 11 on the Fano scheme of lines of a cubic fourfold.

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