On symplectic automorphisms of hyper-Kähler fourfolds of K3[2] type

Abstract

The present paper proves that finite symplectic groups of automorphisms of \hk fourfolds deformation equivalent to the Hilbert scheme of two points on a $K3$ surface are contained in the simple group $Co_1$. Then we give an example of a symplectic automorphism of order 11 on the Fano scheme of lines of a cubic fourfold.