The moduli space of points in quaternionic projective space

Abstract

Let $\mathcal{M}\left(n,m;{\mathbb{F\mathbb{P}}}^n\right)$ be the configuration space of $m$-tuples of pairwise distinct points in ${\mathbb{F\mathbb{P}}}^n$, that is, the quotient of the set of $m$-tuples of pairwise distinct points in ${\mathbb{F\mathbb{P}}}^n$ with respect to the diagonal action of $\text{P}\text{U}(1,n;\mathbb{F})$ equipped with the quotient topology. In this paper, by mainly using the rotation-normalized and the block-normalized algorithms, we construct the parameter spaces of both $\mathcal{M}\left(n,m;\partial {\mathbf{H}}_{\mathrm{ℍ}}^n\right)$ and $\mathcal{M}\left(n,m;\mathrm{\mathbb{P}}\left(V_{+}\right)\right)$, respectively.