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THE MODULI SPACE OF POINTS IN THE BOUNDARY OF QUATERNIONIC HYPERBOLIC SPACE

Gou, Gaoshun 大阪大学 DOI:10.18910/77233

2020.10

概要

Let F_1(n,m) be the PSp(n, 1)-configuration space of ordered m-tuple of pairwise distinct points in the boundary of quaternionic hyperbolic n-space ∂𝗛^n_H , i.e., the m-tuple of pairwise distinct points in ∂𝗛^n_H up to the diagonal action of PSp(n, 1). In terms of Cartan’s angular invariant and cross-ratio invariants, the moduli space of F1(n,m) is described by using Moore’s determinant. We show that the moduli space of F_1(n,m) is a real 2m^2 − 6m + 5 − Σ^<m−n−1> _<i=1> ( ^<m−2>_<n−1+i>) dimensional subset of a algebraic variety with the same real dimension when m > n+1.

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