$\aleph_0$-categorical strongly minimal compact complex manifolds

Rahim Moosa; Anand Pillay

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arXiv · 1007.0731

$\aleph_0$-categorical strongly minimal compact complex manifolds

Rahim Moosa·Anand Pillay

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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 it is pointed 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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BibTeX RIS

Rahim Moosa, Anand Pillay. 2010-07-05. $\aleph_0$-categorical strongly minimal compact complex manifolds. https://arxiv.org/abs/1007.0731

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