If X is a strongly minimal set (of finite differential dimension) in a differentially closed field, then exactly one of the following is true of X

• there is an algebraic curve Y over the constants C and a finite-to-one definable function f:X → Y,
• there is a finite-to-finite definable correspondence between X and some Manin kernel of an abelian variety, or
• X has trivial combinatorial geometry.

Moreover, there are examples of each kind of combinatorial geometry.

Hrushovski and Masonari Itai have shown that "most" strongly minimal sets of differential dimension one (in DCF_0,1) are trivial and have ℵ₀-categorical induced structure.