A surface of degree $24$ with $1440$ singularities of type $D\_4$

TL;DR

The paper constructs a degree 24 algebraic surface with 1440 D4-type singularities using invariant theory of a specific reflection group, advancing the understanding of complex surface singularities.

Contribution

It introduces a new explicit construction of a high-degree surface with a large number of specific singularities via invariant algebra methods.

Findings

Constructed a degree 24 surface with 1440 D4 singularities

Utilized invariant algebra of the G_{32} reflection group

Demonstrated the surface's singularity structure explicitly

Abstract

Using the invariant algebra of the reflection group denoted by $G\_{32}$ in Shephard-Todd classification, we construct three irreducible surfaces in $P^3$ with many singularities: one of them has degree $24$ and contains $1440$ quotient singularities of type $D\_4$.