Finite Symplectic Actions on the K3 Lattice

Abstract

In this paper, we study finite symplectic actions on K3 surfaces X, i.e. actions of finite groups G on X which act on H^{2,0}(X) trivially. We show that the action on the K3 lattice H^2(X,Z) induced by a symplectic action of G on X depends only on G up to isomorphism, except for five groups.

46 pages. #13, #19, #25 and #37 in Table 10.2, and #62 in Table 10.3 were corrected

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• Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups