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$ \aleph_0$-categorical strongly minimal compact complex manifolds


Authors: Rahim Moosa and Anand Pillay
Journal: Proc. Amer. Math. Soc. 140 (2012), 1785-1801
MSC (2010): Primary 03C98; Secondary 32J27
DOI: https://doi.org/10.1090/S0002-9939-2011-11028-1
Published electronically: September 7, 2011
MathSciNet review: 2869164
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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, 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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Additional Information

Rahim Moosa
Affiliation: Department of Pure Mathematics, University of Waterloo, Ontario N2L 3G1, Canada

Anand Pillay
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

DOI: https://doi.org/10.1090/S0002-9939-2011-11028-1
Received by editor(s): July 5, 2010
Received by editor(s) in revised form: January 24, 2011
Published electronically: September 7, 2011
Additional Notes: The first author was partially supported by an NSERC Discovery Grant
The second author was partially supported by EPSRC grant EP/F009712/1, a Marie Curie Chair, as well as the Humboldt Foundation. He would also like to thank Daniel Huybrechts for some helpful conversations during a visit to Bonn in April 2007
Communicated by: Julia Knight
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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