A dodecic surface with 320 cusps

TL;DR

This paper constructs a degree 12 invariant of a complex reflection group, resulting in a surface with 320 singularities, setting a new record for dodecic surfaces.

Contribution

It introduces a new invariant leading to a dodecic surface with more singularities than previously known.

Findings

Constructed a degree 12 invariant for G_{29}

Produced a surface with 320 A_2 singularities

Sets a new record for dodecic surface singularities

Abstract

We construct a degree $12$ homogeneous invariant of the complex reflection group $G_{29}$ (in Shephard-Todd's notation) whose associated surface has 320 singularities of type $A_2$, improving previous records for dodecic surfaces.