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Preprint Number 241
241. Rahim Moosa
A model-theoretic counterpart to Moishezon morphisms
Submission date: 27 April 2010.
The notion of being Moishezon to a set of types, a natural strengthening of internality motivated by complex geometry, is introduced. Under the hypothesis of Pillay's  canonical base property, and using results of Chatzidakis , it is shown that if a stationary type of finite U-rank at least two is almost internal to a nonmodular minimal type and admits a diagonal section, then it is Moishezon to the set of nonmodular minimal types. This result is inspired by Campana's  first algebraicity criterion in complex geometry. Other related abstractions from complex geometry, including coreductions and generating fibrations are also discussed.
Mathematics Subject Classification: 03C45, 03C98, 32J27
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