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Some model theory of compact complex spaces

We make several observations about the category C of compact complex manifolds, considered as a many-sorted structure of finite Morley rank. We also point out that the Mordell-Lang conjecture holds for complex tori: if A is a complex torus, Γ a finitely generated subgroup of A, and X an analytic subvariety of A, then X ∩ Γ is a finite union of translates of subgroups of A. This is implicit in the literature but we give an elementary reduction to the abelian variety case. We discuss analogies between C and the category of finite dimensional differential algebraic sets. (A brief survey of the Mordell-Lang conjecture and model-theoretic contributions is also included.)