Definable sets in generic complex tori (Q1919527)

A complex torus \(M\) is a connected compact complex manifold with complex analytic group structure (a compact complex Lie group). For a complex torus \(M\) of dimension (as a complex manifold) \(\geq 2\), suppose that \(M\) is strongly minimal as a structure equipped with predicates for analytic subsets of \(M\), then \(M\) is locally modular. The proof uses elementary complex analytic arguments to show directly that every irreducible analytic subspace of \(M^m\) is a coset. As a consequence, and \(n\)-dimensional generic complex torus \((n\geq 2)\) is a locally modular strongly minimal structure.