Abstract:
It is shown that the space of finite-to-finite holomorphic correspondences on an OT-manifold is discrete.
When the OT-manifold has no proper infinite complex-analytic subsets, it then follows by known model-theoretic results that its cartesian powers have no interesting complex-analytic families of subvarieties.
The methods of proof, which are similar to [Moosa, Moraru, and Toma "An essentially saturated surface not of Kähler-type", Bull. of the LMS, 40(5):845-854, 2008], require studying finite unramified covers of OT-manifolds.
Key Words: Complex subvariety, correspondence, essential saturation, OT-manifold, strongly minimal compact complex manifold.
2000 Mathematics Subject Classification: Primary: 32J18, 03C98.
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