K3 surfaces with non-symplectic automorphisms of prime order

Abstract

In this note we present the classification of non-symplectic automorphisms of prime order on K3 surfaces, i.e.we describe the topological structure of their fixed locus and determine the invariant lattice in cohomology. We provide new results for automorphisms of order 5 and 7 and alternative proofs for higher orders. Moreover, for any prime p, we identify the irreducible components of the moduli space of K3 surfaces with a non-symplectic automorphism of order p.

28 pages; With an appendix by Shigeyuki Kondo. We add Smith exact sequences in the study of the fixed locus. To appear in Math. Z