ℵ₀-categorical strongly minimal compact complex manifolds

Moosa, Rahim; Pillay, Anand

doi:10.1090/S0002-9939-2011-11028-1

$\aleph _0$-categorical strongly minimal compact complex manifolds
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Proc. Amer. Math. Soc. 140 (2012), 1785-1801 Request permission

Abstract:

Essential $\aleph _0$-categoricity; i.e., $\aleph _0$-categoricity in some full countable language, is shown to be a robust notion for strongly minimal compact complex manifolds. Characterisations of triviality and essential $\aleph _0$-categoricity are given in terms of complex-analytic automorphisms in the simply connected case and correspondences in general. As a consequence, we point out that an example of McMullen yields a strongly minimal compact Kähler manifold with trivial geometry but which is not $\aleph _{0}$-categorical, giving a counterexample to a conjecture of the second author and Tom Scanlon.

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