Key points are not available for this paper at this time.
We introduce a compact moduli scheme of marked noncommutative cubic surfaces as the GIT moduli scheme of relations of a quiver associated with a full strong exceptional collection on a cubic surface. It is a toric variety containing the configuration space of six points on a plane in general position as a locally closed subvariety, and birationally parametrizes a class of AS-regular Z-algebras.
Abdelgadir et al. (Fri,) studied this question.