Complex reflection groups and K3 surfaces II. The groups $G_{29}$, $G_{30}$ and $G_{31}$

Abstract

We study some K3 surfaces obtained as minimal resolutions of quotients of subgroups of special reflection groups. Some of these were already studied in a previous paper by W. Barth and the second author. We give here an easy proof that these are K3 surfaces, give equations in weighted projective space and describe their geometry.