On projective K3 surfaces $\mathcal{X}$ with $\mathrm{Aut}(\mathcal{X})=(\mathbb{Z}/2\mathbb{Z})^2$

Adrian Clingher; Andreas Malmendier; Xavier Roulleau

doi:10.1512/iumj.2025.74.60493

paper

On projective K3 surfaces $X$ with $Aut (X) = (Z /2 Z)^{2}$

arXiv:2305.08959 · doi:10.1512/iumj.2025.74.60493

Abstract

We prove that every K3 surface with automorphism group $(Z /2 Z)^{2}$ admits an explicit birational model as a double sextic surface. This model is canonical for Picard number greater than 10. For Picard number greater than 9, the K3 surfaces in question possess a second birational model, in the form of a projective quartic hypersurface, generalizing the Inose quartic.

28 pages, 10 figures

On projective K3 surfaces X with Aut(X)=(Z/2Z)2

Abstract

On projective K3 surfaces $X$ with $Aut (X) = (Z /2 Z)^{2}$