Symplectic automorphisms of prime order on K3 surfaces

2006

75 citations recorded by the source corpus.

Abstract We study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients (by a result of Nikulin this action is independent on the choice of the K3 surface). With the help of elliptic fibrations we determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the Coxeter–Todd lattice in the case of automorphism of order three.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aab4b262f30dd3b64d1a48beeb7a77d23f1c49d6

Citations in the corpus

• Nikulin involutions on K3 surfaces (2006, background): “He proves that when the group G is cyclic and acts symplectically, then G = Z=nZ, 1 n 8. Symplectic automorphisms of K3 surfaces of orders three, v e and seven are investigated in the paper [ GS ].”
• Elliptic Fibrations and Symplectic Automorphisms on K3 Surfaces (2008, methodology): “[11, 12]), in fact they give information on the coarse moduli space of algebraic K3 surfaces with symplectic automorphisms.”
• Non-symplectic automorphisms of order 3 on K3 surfaces (2008, background): “In [ 12, Theorem 5.1 ] it is proved that the orthogonal complement of the fixed lattice of such automorphisms is isomorphic to K12.”
• Lectures on K3 Surfaces (2016, background): “This was generalized by Garbagnati and Sarti in [199] to symplectic automorphisms of prime order p.”