2023/10/11 by Silversmith, Rob
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2310.07377
The cross-ratio degree problem counts configurations of n points on P1 with n-3 prescribed cross-ratios. Cross-ratio degrees arise in many corners of combinatorics and geometry, but their structure is not well-understood in general. Interestingly, examining various special cases of the problem can yield combinatorial structures that are both diverse and rich. In this paper we prove a simple closed formula for a class of cross-ratio degrees indexed by triangulations of an n-gon; these degrees are connected to the geometry of the real locus of M0,n, and to positive geometry.