The Dihedral Group D5 as a Group of Symplectic Automorphisms on K3 Surfaces
نویسنده
چکیده
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. We also give an elementary construction of L.
منابع مشابه
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...
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