Hypercomplex analytic spaces and schemes

Abstract

We propose definitions of hypercomplex analytic spaces and hypercomplex schemes. We show that such a hypercomplex space is canonically associated to the quotient of a hypercomplex manifold by a finite group action.

v.3: a clarification added in the introduction; v.2: added a result (Proposition 2.10) clarifying the structure of normal hypercomplex spaces $X$ such that Sing$(X)$ does not disconnect $X$ locally; the introduction has been partly rewritten, and a reference added