Automorphisms of the symplectic modular group

Symplectic Automorphisms and the Picard Group of a K3 Surface

Let X be a K3 surface, and let G be a finite group acting on X by automorphisms. The action of G on X induces an action on the cohomology of X . We assume G acts symplectically: that is, G acts as the identity on H(X). In this case, the minimum resolution Y of the quotient X/G is itself a K3 surface. Nikulin classified the finite abelian groups which act symplectically on K3 surfaces by analyzi...

The Dihedral Group D5 as a Group of Symplectic Automorphisms on K3 Surfaces

We prove that if a K3 surface X admits Z/5Z as a group of symplectic automorphisms, then it actually admits D5 as a group of symplectic automorphisms. The orthogonal complement to the D5-invariants in the second cohomology group of X is a rank 16 lattice, L. It is known that L does not depend on X: we prove that it is isometric to a lattice recently described by R. L. Griess Jr. and C. H. Lam. ...

The Dihedral Group D5 as Group of Symplectic Automorphisms on K3 Surfaces

We prove that if a K3 surface X admits Z/5Z as group of symplectic automorphisms, then it actually admits D5 as group of symplectic automorphisms. The orthogonal complement to the D5-invariants in the second cohomology group of X is a rank 16 lattice, L. It is known that L does not depend on X: we prove that it is isometric to a lattice recently described by R. L. Griess Jr. and C. H. Lam. We a...

Some Remarks on Symplectic Automorphisms

Symplectic Automorphisms on Kummer Surfaces

Nikulin proved that the isometries induced on the second cohomology group of a K3 surface X by a finite abelian group G of symplectic automorphisms are essentially unique. Moreover he computed the discriminant of the sublattice of H(X,Z) which is fixed by the isometries induced by G. However for certain groups these discriminants are not the same of those found for explicit examples. Here we de...