-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 | References | Similar Articles | Additional Information

Abstract: *Essential* -categoricity; i.e., -categoricity in some full countable language, is shown to be a robust notion for strongly minimal compact complex manifolds. Characterisations of triviality and essential -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 -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.