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 $U^3\oplus E_8(-1)^2$ 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.
Elliptic Fibrations and Symplectic Automorphisms on K3 Surfaces / A. Garbagnati, A. Sarti. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - 37:10(2009 Oct), pp. 3601-3631. [10.1080/00927870902828785]
Elliptic Fibrations and Symplectic Automorphisms on K3 Surfaces
A. GarbagnatiPrimo
;
2009
Abstract
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 $U^3\oplus E_8(-1)^2$ 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.
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