# 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.