The O-minimal Zilber Conjecture in Higher Dimensions

We prove the higher dimensional case of the o-minimal variant of Zilber's Restricted Trichotomy Conjecture. More precisely, let R be an o-minimal expansion of a real closed field, let M be an interpretable set in R, and let M=(M,...) be a reduct of the induced structure on M. If M is strongly minimal and not locally modular, then R(M)=2. As an application, we prove the Zilber trichotomy for all strongly minimal structures interpreted in the theory of compact complex manifolds.