On Automorphisms Group of Some K3 Surfaces
نویسنده
چکیده
In this paper we study the automorphisms group of some K3 surfaces which are double covers of the projective plane ramified over a smooth sextic plane curve. More precisely, we study some particlar case of a K3 surface of Picard rank two. Introduction K3 surfaces which are double covers of the plane ramified over a plane sextic are classical objects. In this paper we determine the automorphisms group of some of these surfaces. More precisely, we restrict to the case of Picard rank two. We study the case of a K3 surface with Picard lattice of rank two with quadratic form given by Qd := (
منابع مشابه
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⊕E8(−1) 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.
متن کاملAutomorphisms of K 3 Surfaces
In this note, we report some progress we made recently on the automorphisms groups of K3 surfaces. A short and straightforward proof of the impossibility of Z/(60) acting purely non-symplectically on a K3 surface, is also given, by using Lef-schetz fixed point formula for vector bundles.
متن کاملThe 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...
متن کاملMaximal Subgroups of the Mathieu Group M23 and Symplectic Automorphisms of Supersingular K3 Surfaces
We show that the Mathieu groups M22 and M11 can act on the supersingular K3 surface with Artin invariant 1 in characteristic 11 as symplectic automorphisms. More generally we show that all maximal subgroups of the Mathieu group M23 with three orbits on 24 letters act on a supersingular K3 surface with Artin invariant 1 in a suitable characteristic.
متن کاملAutomorphisms on K3 Surfaces with Small Picard Number
In this paper, we demonstrate via an example a variety of techniques both general and ad hoc that can be used to find the group of automorphisms of a K3 surface. Introduction Given a K3 surface X/k over a number field k, what is its group of automorphisms A = Aut(X/k)? In this paper, we offer some ideas of how to answer this natural question, and demonstrate these ideas by applying them to a pa...
متن کامل