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arXiv · 2408.08049

A note on subvarieties of powers of OT-manifolds

Rahim Moosa·Matei Toma
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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 K\"ahler-type", {\em Bull. of the LMS}, 40(5):845--854, 2008], require studying finite unramified covers of OT-manifolds.

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Rahim Moosa, Matei Toma. 2024-08-15. A note on subvarieties of powers of OT-manifolds. https://arxiv.org/abs/2408.08049

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