The moduli space of points in quaternionic projective space

2017/05/18 by Cao, Wensheng
#32H20 #32M15 #53C17 #57M50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.06458

Abstract

Let M(n,m;\F \bpⁿ) be the configuration space of m-tuples of pairwise distinct points in \F \bpⁿ, that is, the quotient of the set of m-tuples of pairwise distinct points in \F \bpⁿ with respect to the diagonal action of \rm PU(1,n;\F) equipped with the quotient topology. It is an important problem in hyperbolic geometry to parameterize M(n,m;\F \bpⁿ) and study the geometric and topological structures on the associated parameter space. In this paper, by mainly using the rotation-normalized and block-normalized algorithms, we construct the parameter spaces of both M(n,m; \bhq) and M(n,m;\bp(V₊)), respectively.

Related

• The Moduli Space of Points in the Boundary of Quaternionic Hyperbolic Space
• Moduli of triples of points in quaternionic hyperbolic geometry
• The Geometry of Polygons in R⁵ and Quaternions
• Point Configurations and Translations
• Resolution of Diagonals and Moduli Spaces