On the Supersingular reduction of Cubic fourfolds with Complex Multiplication

Source abstract

If $X$ is a K3 surface with complex multiplication by a CM field $E$, Kazuhiro Ito proved that the height of the reduction of $X$ in characteristic $p>0$, and its Artin invariant if it is supersingular, can be computed from the decomposition of $p$ in $E$. We present analogous results for cubic fourfolds by using the main theorem of complex multiplication for cubic fourfold, proved by Rikuto Ito.