The Moduli Space of Points in the Boundary of Quaternionic Hyperbolic Space

Abstract

Let ${\mathcal{F}}_1(n,m)$ be the space of ordered m-tuples of pairwise distinct points in $\partial {\mathbf{H}}_{\mathbb{H}}^n$ up to its isometry group $PSp(n,1)$. It is a real $2m^2-6m+5-{\sum }_{i=1}^{m-n-1}\left(\genfrac{}{}{0ex}{}{m-2}{n-1+i}\right)$ dimensional algebraic variety when $m>n+1$. In this paper, we construct and describe the moduli space of ${\mathcal{F}}_1(n,m)$, in terms of the Cartan's angle and cross-ratio invariants, by applying the Moore's determinant.

18 pages

References in corpus (1)

• The moduli space of points in quaternionic projective space

Cited by in corpus (1)

• The moduli space of points in quaternionic projective space