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

TL;DR

This paper investigates certain K3 surfaces derived from quotients of subgroups of specific complex reflection groups, providing new proofs, explicit equations, and geometric descriptions to enhance understanding of their structure.

Contribution

It offers a simplified proof that these quotients are K3 surfaces, along with explicit equations and geometric insights, expanding on prior work by Barth and the second author.

Findings

Confirmed these quotients are K3 surfaces

Derived explicit equations in weighted projective space

Described geometric properties of the surfaces

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.