The moduli space of K3 surfaces with a purely non-symplectic automorphism of order is one dimensional exactly when or . In this paper we classify and give explicit equations for the very general members of the irreducible components of maximal dimension of such moduli spaces. In particular, we show that there is a unique one-dimensional component for , three irreducible components for and two components in the remaining cases.
Cite this article
Michela Artebani, Paola Comparin, María Elisa Valdés, Non-symplectic automorphisms of K3 surfaces with one-dimensional moduli space. Rev. Mat. Iberoam. 38 (2022), no. 4, pp. 1161–1198DOI 10.4171/RMI/1326