A description of the outer automorphism of S_6, and the invariants of six points in projective space

TL;DR

This paper leverages the outer automorphism of S_6 to clarify the invariant theory related to six points in projective spaces of dimensions one to three.

Contribution

It provides a novel, simplified description of the outer automorphism of S_6 and applies it to describe invariants of six points in various projective spaces.

Findings

Clear description of the outer automorphism of S_6

Simplified invariant theory for six points in P^1, P^2, and P^3

Enhanced understanding of symmetries in projective configurations

Abstract

We use a simple description of the outer automorphism of S_6 to cleanly describe the invariant theory of six points in P^1, P^2, and P^3.