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

Arjun Maniyar

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.

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

Abstract

The cross-ratio degree problem asks for the number of configurations of points in that satisfy 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 is equal to 4.
Paper Structure (7 sections, 21 equations, 2 tables)

This paper contains 7 sections, 21 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Calculating cross-ratio degree
  3. Computing all biadjacency matrices
  4. Acknowledgements
  5. Appendix
  6. Counting number of $n$-uniform hypergraphs
  7. Matrices and other data

Theorems & Definitions (7)

  • Definition 1.1
  • Definition 1.2
  • Remark 1.1
  • Example 2.1
  • Remark 2.1
  • Remark 2.2
  • Definition 4.1