Isolated types of finite rank: an abstract Dixmier-Moeglin equivalence

Suppose $T$ is totally transcendental and every minimal non-locally-modular type is nonorthogonal to a nonisolated minimal type over the empty set. It is shown that a finite rank type $p=tp(a\mathrm{/}A)$ is isolated if and only if $a$ is independent from $q(\mathcal{U})$ over $Ab$ for every $b\in \operatorname{acl}(Aa)$and$q\in S(Ab)$ nonisolated and minimal. This applies to the theory of differentially closed fields – where it is motivated by the differential Dixmier-Moeglin equivalence problem – and the theory of compact complex manifolds.