Geometry ag.algebraica: modular space of almost complex structures as an algebra-geometric object

Leave $ M $ To be a real closed analytical variety of dimension. $ 2n $. Is it possible to give meaning to the space of modules of almost complex real analytical structures in $ M $ as an algebro-geometric object (probably a very non-Noetherian one)? Can this be used to obtain a new perspective on, for example, the almost complex structures of Fredholm-regular? I do not think this is particularly useful, but I think that if it's possible, it's worth doing just for fun.

Perhaps a terribly non-canonical way of doing this is to build a subschema of $ bigcup_ {p in M} mathrm {Mat} (2n, 2n) $ (Choose a base for the tangent beam fiber at some point, choose a connection to produce bases at nearby points, somehow understand the real analytical state and then take the disappearance scheme from the "polynomial" equation $ J ^ 2 = – mathrm {Id} $ and I hope that this can be made to work worldwide). With luck, someone else thought of a better way.