Finite subgroups of automorphisms of K3 surfaces

Abstract We give a complete classification of finite subgroups automorphisms K3 surfaces up to deformation. The is in terms Hodge theoretic data associated certain conjugacy classes the orthogonal group lattice. moduli theory surfaces, particular surjectivity period map and strong Torelli theorem allow us interpret this datum geometrically. Our approach computer aided involves Hermitian lattices over number fields.