Cross-ratios and perfect matchings

Abstract: I’ll describe a simple process from algebraic geometry that takes in a collection of $4$-element subsets $S_1,S_2,…,S_{n-3}$ of $[n]$, and outputs a nonnegative integer called a cross-ratio degree. I’ll discuss several interpretations of cross-ratio degrees in algebra, algebraic geometry, and tropical geometry, and present a combinatorial algorithm for computing them, due to C. Goldner. I’ll then present a perhaps-surprising upper bound for cross-ratio degrees in terms of matchings.

combinatorics

Audience: researchers in the topic

Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.