On quaternionic tori and their moduli space (Q1656209)

Summary: 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 \textit{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.