On symplectic automorphisms of hyperkähler fourfolds of K3^[2] type

Abstract

The present paper proves that finite symplectic groups of automorphisms of hyperkähler fourfolds deformation equivalent to the Hilbert scheme of two points on a $K3$ surface are contained in the simple group $C{o}_1$. Then we give an example of a symplectic automorphism of order 11 on the Fano scheme of lines of a cubic fourfold.

arXiv commentFinal version, to appear on Mich. Math. J

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