Seven points in general linear position

TL;DR

This paper computes the cohomology groups of the space of seven points in general linear position, revealing their structure as symmetric group representations through equivariant point counts over finite fields.

Contribution

It provides a detailed calculation of cohomology groups for seven points in general linear position and discusses the case of eight points.

Findings

Cohomology groups explicitly determined for seven points.

Representation structure as symmetric group representations.

Insights into the case of eight points.

Abstract

We determine the cohomology groups of the space of seven points in general linear position as representations of the symmetric group on seven elements by making equivariant point counts over finite fields. We also comment on the case of eight points.