ELLIPTIC FIBRATIONS AND SYMPLECTIC AUTOMORPHISMS ON K3 SURFACES

Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice U(3) circle plus E(8)(-1)(2) depends only on the group but not on the K3 surface. For all the groups in the list of Nikulin we compute the invariant sublattice and its orthogonal complement by using some special elliptic K3 surfaces.