K3 surfaces with non-symplectic automorphisms of prime order

In this paper we present the classification of non-symplectic automorphisms of prime order on K 3 surfaces, i.e. we describe the topological structure of their fixed locus and determine their 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 K 3 surfaces with a non-symplectic automorphism of order p .