K3 surfaces with real or complex multiplication

Eva Bayer-Fluckiger, Bert van Geemen, Matthias Schütt

Published 2024-01-08Version 1

Let $E$ be a totally real number field of degree $d$ and let $m \geq 3$ be an integer. We show that if $md \leq 21$ then there exists an $m-2$-dimensional family of complex projective $K3$ surfaces with real multiplication by $E$. An analogous result is proved for CM number fields.