On Quaternionic Tori and their Moduli Spaces

Abstract

Quaternionic tori are defined as quotients of the skew field $\mathbb{H}$ of quaternions by rank-4 lattices. Using slice regular functions, these tori are endowed with natural structures of quaternionic manifolds (in fact quaternionic curves), and a fundamental region in a $12$-dimensional real subspace is then constructed to classify them up to biregular diffeomorphisms. The points of the moduli space correspond to suitable \emph{special} bases of rank-4 lattices, which are studied with respect to the action of the group $GL(4,\mathbb{Z})$, and up to biregular diffeomeorphisms. All tori with a non trivial group of biregular automorphisms - and all possible groups of their biregular automorphisms - are then identified, and recognized to correspond to five different subsets of boundary points of the moduli space.

Published Online 2018-05-24 on Journal of Noncommutative Geometry

Cited by in corpus (5)

• Slice-quaternionic Hopf surfaces
• The harmonicity of slice regular functions
• On a quaternionic Picard theorem
• Slice conformality and Riemann manifolds on quaternions and octonions
• Birational geometry of quaternions