Maximal cross-ratio degree for 8 points in $\mathbb{P}^1$

TL;DR

This paper determines that the maximum number of configurations of 8 points in projective line satisfying certain cross-ratio conditions is exactly 4, refining previous lower bounds.

Contribution

It establishes the exact maximal cross-ratio degree for 8 points in projective line, resolving a known lower bound and providing a precise value.

Findings

Maximal cross-ratio degree for 8 points is 4

Confirmed previous lower bound as exact value

Contributes to understanding of configuration counts in projective geometry

Abstract

The cross-ratio degree problem asks for the number of configurations of $n$ points in $\mathbb{P}^1$ that satisfy $n-3$ specified cross-ratio conditions. It is known that the maximal cross-ratio degree for 8 points is at least 4. In this paper, we will see that the maximal cross-ratio degree for 8 points in $\mathbb{P}^1$ is equal to 4.