Submission date: 27 April 2010.

Abstract:

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 [6] canonical base property, and using results of Chatzidakis [2], 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 [1] “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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